2019新初一有理数计算700题

2022年​小学升学考试冲刺复习卷-数学​

第二届经济金融数据分析与建模大赛报名表

附件1第二届经济金融数据分析与建模大赛报名表团队名称团队人数团队负责人学校学院专业联系电话邮箱成员信息：姓名学校专业年级联系电话本人承诺自愿参与，以上填写信息真实有效。负责人签字：日期：年月日

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

简介：41.-5852.-845993.-1054.65.0.4146.277.-108.259.910.13.3411.-22712.-413.31.514.415.17516.251217.718.3119.8320.4.7321.501422.323.4.2224.2725.626.503 27.63128.1511129.4110230.11331.154000532.6733.1181034.4134535.436.2537.1138.11339.640.5241.042.6143.644.92445.3200246.2147.4 148.62149.57250.451.052.453.2054.30255.4356.757.1060158.259.1060.27161.6162.28163.16164.85365.2066.26167.168.812369.9670.4 571.272.511173.2259974.100175.276.877.13178.24579.280.45181.28482.2783.5584.285.786.1587.4888.689.8390.291.4192.2593.294.10095.696.250 297.998.5.0399.0100.899.5 101.1.995102.-40103.35.364104.-45105.199.51106.-156107.12452004108.-20042005109.-48110.31111.-31112.75113.425114.-2431115.-42116.-1516117.15118.5119.49 8120.542121.253122.8123.6124.0125.645126.24127.486128.0.8527129.16130.2961131.1827132.2133.3134.144135.1539136.20137.80138.71139.57140.3 14141.-91142.-3143.260144.25802007145.20072008146.26762147.3148.3149.0150.3.361151.-7152.73153.343154.57514155.1529156.236157.0.43158.-641159.103160.43.6161.94 1162.113163.1164.24.57165.4550166.77231167.31482168.631169.43170.15171.01172.2635173.361174.215175.21176.4177.-2178.-1179.0180.-4.48181.261182.10.08 183.3.47184.8.751185.4186.463187.5188.113189.121190.116191.90192.-181193.5194.0195.-235196.481197.315198.-8199.-45200.28 9201.7202.612203.71204.-7205.25206.31.3207.1201208.127209.6210.99211.161212.6213.113214.2025215.0216.903217.4218.123219.2220.851221.22 222.8223.229224.16125225.64226.31227.01228.55229.20230.27231.6232.10233.11234.4235.14236.121237.7235238.124239.3240.717241.2242.24243.501244.2245.11.04246.7 247.5248.10249.10601250.83251.1252.614253.27254.138255.89256.-2257.0258.14259.851260.1753261.43262.23263.64264.4265.251266.61267.22169268.196269.58 270.9056271.15272.31273.24125274.643275.50276.31277.48278.7227279.24280.25281.161282.25283.85284.11285.10286.22108287.7288.3421289.5290.0291.0292.0293.999216294.3 1295.81296.22297.0298.30.3299.2300.20 301.43302.11303.1.03304.8305.50306.8.5307.661308.3309.35310.6999311.19995312.481313.315314.8315.45316.289317.7318.31.3319.120320.903321.41322.125323.6324.99325.16 1326.613327.2025328.029329.6330.8.53331.4332.1333.7334.3335.7336.07337.16338.0339.81340.-434341.4191342.32343.91344.82345.25346.38.1347.1.5 1348.600349.0.320350.31351.8561352.6353.611354.225334355.3356.1.022357.43358.2359.1360.10361.9.7688362.315363.05364.72365.13319993366.111367.16368.51369.34 11370.91371.21372.565844373.43374.-104.727375.900376.199000377.0378.1379.05380.2125381.204382.125383.36189384.820073-3385.2386.0387.389732611388.20200389.101390.2 391.24755392.4393.482394.253395.12516396.2397.0125398.3399.03400.8 401.25402.9.5403.30404.13405.9406.172912407.408.2409.24331410.10411.5412.1321517413.17414.415.5241416.9417.418.121419.1420.58421.368191422.423.32.8424.496425.34426.50427.3085428.1429.14.5430.111315431.72432.433.448459434.435.3436.86502437.1438.24439.1005999765440.441.442.20097671444.200443.15445.121015021446.447.12448.1510132 142449.450.28451.295 1111452.原式1121231234123456722212334781111111222334781721841453.1011111454.原式25588111114141711111111111325588111114141711153217341111111455.原式41335355720012003200320051111004003413200320051204804579161182901111456.原式1133557791331.2540.83714611111111233579131234631823=244293611111457.原式1232026122042011111210122334452021111111121012233420211202101210212111111458.原式200820092010201120123669912121515181111111201059122356510050541325375117459.原式26153577有理数计算1 学而思初中优秀教学体系1111111112233557711110111111111111460.原式13355779911111313151111111112132352131511172115151111461.原式1111261299001119912239910011111991223991001991100198100111111111462.原式2122323346778788911121289351444949463.1980038625464.3400323200465.9603100100100100111466.原式…(…)1232343459910010123341001011111151100()()24221010021011011111111467.原式312323423434578989101111193123891021601111111468.原式3[(…)]312323423434517181918192011319201113912318192018192068403234316469.原式1232348910有理数计算2 学而思初中优秀教学体系111128321232348910123234891011111111113221223233489910233491031111111122129102334910311117112322290210460515571719470.23434589109101123349102343459101111111134244535101191111111134451011243591111111111111111111344510112243546810911111111181283131122103113325335531所以原式1155651．55222234512471.原式1234523456345671011121314154264374101441234523456345671011121314111123434545611121344441234523456345671011121314111111122334344511121213111111123423452345345610111213111213141111122312131234111213141111177111122121324111213148111213148211141175830861612349472.原式22323423452341021314110122323423410111111112223232342349234910有理数计算3 学而思初中优秀教学体系136287991234910362880013141516171473.原式12123123412345123456123456711111112121231231234123456711112121234567150391504050402399474.原式1231234123100314110011231234123100111111121231231234123991231001111121231002100!234550475.原式＝＋＋＋＋…＋1336610101512251275111111111274＝（）＋（）＋（）＋（）＝1336610122512751275211311476.，，……，1(12)112(12)(123)1212310011，所以(1299)(12100)1299121001原式1121001504915050505023410477.原式1()13366104555111111111336610455511115555111111478.原式()()()()()()244668810101212141111111111111()2446688101012121421113()2142141111311124479.1(1)(1)，1(1)(1)，……所以，2222222333331324485015025原式22334949249492222222221324387480.原式2222222212233478有理数计算4 学而思初中优秀教学体系11111111222222222334781631286422222481.原式1111122222315171199311995122299724461994199611111199724461994199611997997997219961996222222131024203534104204344482.，，，……由于2，2，2，2222133184115338815154444可见原式222222222131419911111298413243598100111111111964123243598100111196212991001991963299004751198495022221246100483.原式222242141611001111111111222242141611001111115041335579910111111111150142335579910111115063501501242101410110156677889910111111113484.()…()5667788991056679105101036233445566736111111485.原式=…=4572334455667572334671325711111121486.原式11111534578453738571231111112113487.原式357344547566711112123131113333665557774444有理数计算5 学而思初中优秀教学体系111111111111111488.原式23303141317717430341431111111112233743475791113153489.原式71861220304256811111111782334788111178828821111023344556677889910490.原式12334455667788991011111111111111111()()()()()()()()2334455667788991011312105111111112111491.原式45344535564611112452334561232341918192021919492.原式…2173621234318192019120202008111200711493.原式=(…)(…)2008120072200620071200812006200612008111200711=(…)(…)2008120072200620071200812006200611200820082008120072007=(…)(…)20081200722006200712008120062006111111111111=[(…)(…)]2008120072200620071120062006111111111111=[(…)(…)]200812007220062007112006200611111=()2008200720072015028111111111494.原式249835995152991111111112245035495254981111111112450354926274911111111112242435252628485011111111112424352513142450111111111112241235111416245025有理数计算6 学而思初中优秀教学体系1111111111124123511781250251111111111224635810125025111111111124635456502511491502550315171131495.原式335357357911131111111335357911335357911131135791113135134135135341199222224422496.135357171921133535571719192189224221335571719192188912222422所以原式1335171913355717191921921512133379192113399399497.2498.-3499.-3500.-17有理数计算7 8501.2502.131503.1504.2505.1506.911507.508.1148510.3509.7511.-1512.5513.5514.125515.516.91224517.518.817519.3520.19521.1522.416523.8524.344525.526.335552528.527.18515529.无解530.5617531.29532.25533.8534.3 17535.2536.2517537.5538.634539.1540.19541.3542.112543.1544.561545.546.772547.17548.5549.11550.03552.2551.5691553.554.23107555.556.1141558.2557.-4183559.560.1152562.7561.713563.564.1111 1565.9566.61531568.567.212517569.570.15253571.4 x1x4572.573.y3y110xx67574.575.y43y7x2x4576.577.y1y11ax52579.578.y21b3x2x11580.581.y2y19x1x4582.7583.yy3329x22x3585.584.75y1y221x2x8586.587.3y28y2x7x370588.589.y0y1103349xx1023590.591.4916yy1023 9xx25592.593.y93y5x6x2594.595.y9y1x7x1597.596.y1y1x35x2599.598.y14y0.4x18x2601.600.19y6y2x5x1602.2603.yy135x1x605.604.2y1y1x2x5606.607.y1y7x2x3608.609.y2y8x5x4610.611.y16y2x2x5612.613.y1y7 x3x5614.1615.yy33x4x3616.617.y1y2x2x0618.619.y2y51xx4621.2620.y5y1 622.x1623.x2624.x5523625.x626.x1627.x779630.x4628.x629.x32631.x17632.x0633.x1715635.x3634.x16636.x710131638.x3639.x637.x97640.x2641.x4642.x2643.x4644.x3645.x320646.x4647.x1648.x39649.x6650.x2651.x25653.x82652.x654.x755655.x656.x7657.x334659.x6660.x3658.x291661.x5662.x2663.x271665.x1664.x666.x271667.x13668.x2669.x2 12672.x2670.x671.x95116673.x674.x675.x3435676.x2677.x10678.x411679.x1680.x3681.x77683.x1684.x1682.x525687.x2685.x4686.x2355689.x690.x8688.x421619691.x692.x3693.x75 1694.x5695.x3696.11x33697.x2698.14x699.21x2700.28x701.23x702.x22703.x704.x3705.21x35706.x4707.x6708.x121709.21x710.x711.x121712.2x713.31x714.无解2715.12x716.x1717.x2718.26x719.42x720.无解721.x4722.12x723.6x131724.x1725.2x726.无解25727.-1x2728.x729.x12730.x2731.42x732.12x7733.x2734.-1x735.x3413736.4x11737.x738.无解2279739.x1740.x2741.x125
简介：41.-5852.-845993.-1054.65.0.4146.277.-108.259.910.13.3411.-22712.-413.31.514.415.17516.251217.718.3119.8320.4.7321.501422.323.4.2224.2725.626.503 27.63128.1511129.4110230.11331.154000532.6733.1181034.4134535.436.2537.1138.11339.640.5241.042.6143.644.92445.3200246.2147.4 148.62149.57250.451.052.453.2054.30255.4356.757.1060158.259.1060.27161.6162.28163.16164.85365.2066.26167.168.812369.9670.4 571.272.511173.2259974.100175.276.877.13178.24579.280.45181.28482.2783.5584.285.786.1587.4888.689.8390.291.4192.2593.294.10095.696.250 297.998.5.0399.0100.899.5 101.1.995102.-40103.35.364104.-45105.199.51106.-156107.12452004108.-20042005109.-48110.31111.-31112.75113.425114.-2431115.-42116.-1516117.15118.5119.49 8120.542121.253122.8123.6124.0125.645126.24127.486128.0.8527129.16130.2961131.1827132.2133.3134.144135.1539136.20137.80138.71139.57140.3 14141.-91142.-3143.260144.25802007145.20072008146.26762147.3148.3149.0150.3.361151.-7152.73153.343154.57514155.1529156.236157.0.43158.-641159.103160.43.6161.94 1162.113163.1164.24.57165.4550166.77231167.31482168.631169.43170.15171.01172.2635173.361174.215175.21176.4177.-2178.-1179.0180.-4.48181.261182.10.08 183.3.47184.8.751185.4186.463187.5188.113189.121190.116191.90192.-181193.5194.0195.-235196.481197.315198.-8199.-45200.28 9201.7202.612203.71204.-7205.25206.31.3207.1201208.127209.6210.99211.161212.6213.113214.2025215.0216.903217.4218.123219.2220.851221.22 222.8223.229224.16125225.64226.31227.01228.55229.20230.27231.6232.10233.11234.4235.14236.121237.7235238.124239.3240.717241.2242.24243.501244.2245.11.04246.7 247.5248.10249.10601250.83251.1252.614253.27254.138255.89256.-2257.0258.14259.851260.1753261.43262.23263.64264.4265.251266.61267.22169268.196269.58 270.9056271.15272.31273.24125274.643275.50276.31277.48278.7227279.24280.25281.161282.25283.85284.11285.10286.22108287.7288.3421289.5290.0291.0292.0293.999216294.3 1295.81296.22297.0298.30.3299.2300.20 301.43302.11303.1.03304.8305.50306.8.5307.661308.3309.35310.6999311.19995312.481313.315314.8315.45316.289317.7318.31.3319.120320.903321.41322.125323.6324.99325.16 1326.613327.2025328.029329.6330.8.53331.4332.1333.7334.3335.7336.07337.16338.0339.81340.-434341.4191342.32343.91344.82345.25346.38.1347.1.5 1348.600349.0.320350.31351.8561352.6353.611354.225334355.3356.1.022357.43358.2359.1360.10361.9.7688362.315363.05364.72365.13319993366.111367.16368.51369.34 11370.91371.21372.565844373.43374.-104.727375.900376.199000377.0378.1379.05380.2125381.204382.125383.36189384.820073-3385.2386.0387.389732611388.20200389.101390.2 391.24755392.4393.482394.253395.12516396.2397.0125398.3399.03400.8 401.25402.9.5403.30404.13405.9406.172912407.408.2409.24331410.10411.5412.1321517413.17414.415.5241416.9417.418.121419.1420.58421.368191422.423.32.8424.496425.34426.50427.3085428.1429.14.5430.111315431.72432.433.448459434.435.3436.86502437.1438.24439.1005999765440.441.442.20097671444.200443.15445.121015021446.447.12448.1510132 142449.450.28451.295 1111452.原式1121231234123456722212334781111111222334781721841453.1011111454.原式25588111114141711111111111325588111114141711153217341111111455.原式41335355720012003200320051111004003413200320051204804579161182901111456.原式1133557791331.2540.83714611111111233579131234631823=244293611111457.原式1232026122042011111210122334452021111111121012233420211202101210212111111458.原式200820092010201120123669912121515181111111201059122356510050541325375117459.原式26153577有理数计算1 学而思初中优秀教学体系1111111112233557711110111111111111460.原式13355779911111313151111111112132352131511172115151111461.原式1111261299001119912239910011111991223991001991100198100111111111462.原式2122323346778788911121289351444949463.1980038625464.3400323200465.9603100100100100111466.原式…(…)1232343459910010123341001011111151100()()24221010021011011111111467.原式312323423434578989101111193123891021601111111468.原式3[(…)]312323423434517181918192011319201113912318192018192068403234316469.原式1232348910有理数计算2 学而思初中优秀教学体系111128321232348910123234891011111111113221223233489910233491031111111122129102334910311117112322290210460515571719470.23434589109101123349102343459101111111134244535101191111111134451011243591111111111111111111344510112243546810911111111181283131122103113325335531所以原式1155651．55222234512471.原式1234523456345671011121314154264374101441234523456345671011121314111123434545611121344441234523456345671011121314111111122334344511121213111111123423452345345610111213111213141111122312131234111213141111177111122121324111213148111213148211141175830861612349472.原式22323423452341021314110122323423410111111112223232342349234910有理数计算3 学而思初中优秀教学体系136287991234910362880013141516171473.原式12123123412345123456123456711111112121231231234123456711112121234567150391504050402399474.原式1231234123100314110011231234123100111111121231231234123991231001111121231002100!234550475.原式＝＋＋＋＋…＋1336610101512251275111111111274＝（）＋（）＋（）＋（）＝1336610122512751275211311476.，，……，1(12)112(12)(123)1212310011，所以(1299)(12100)1299121001原式1121001504915050505023410477.原式1()13366104555111111111336610455511115555111111478.原式()()()()()()244668810101212141111111111111()2446688101012121421113()2142141111311124479.1(1)(1)，1(1)(1)，……所以，2222222333331324485015025原式22334949249492222222221324387480.原式2222222212233478有理数计算4 学而思初中优秀教学体系11111111222222222334781631286422222481.原式1111122222315171199311995122299724461994199611111199724461994199611997997997219961996222222131024203534104204344482.，，，……由于2，2，2，2222133184115338815154444可见原式222222222131419911111298413243598100111111111964123243598100111196212991001991963299004751198495022221246100483.原式222242141611001111111111222242141611001111115041335579910111111111150142335579910111115063501501242101410110156677889910111111113484.()…()5667788991056679105101036233445566736111111485.原式=…=4572334455667572334671325711111121486.原式11111534578453738571231111112113487.原式357344547566711112123131113333665557774444有理数计算5 学而思初中优秀教学体系111111111111111488.原式23303141317717430341431111111112233743475791113153489.原式71861220304256811111111782334788111178828821111023344556677889910490.原式12334455667788991011111111111111111()()()()()()()()2334455667788991011312105111111112111491.原式45344535564611112452334561232341918192021919492.原式…2173621234318192019120202008111200711493.原式=(…)(…)2008120072200620071200812006200612008111200711=(…)(…)2008120072200620071200812006200611200820082008120072007=(…)(…)20081200722006200712008120062006111111111111=[(…)(…)]2008120072200620071120062006111111111111=[(…)(…)]200812007220062007112006200611111=()2008200720072015028111111111494.原式249835995152991111111112245035495254981111111112450354926274911111111112242435252628485011111111112424352513142450111111111112241235111416245025有理数计算6 学而思初中优秀教学体系1111111111124123511781250251111111111224635810125025111111111124635456502511491502550315171131495.原式335357357911131111111335357911335357911131135791113135134135135341199222224422496.135357171921133535571719192189224221335571719192188912222422所以原式1335171913355717191921921512133379192113399399497.2498.-3499.-3500.-17有理数计算7 8501.2502.131503.1504.2505.1506.911507.508.1148510.3509.7511.-1512.5513.5514.125515.516.91224517.518.817519.3520.19521.1522.416523.8524.344525.526.335552528.527.18515529.无解530.5617531.29532.25533.8534.3 17535.2536.2517537.5538.634539.1540.19541.3542.112543.1544.561545.546.772547.17548.5549.11550.03552.2551.5691553.554.23107555.556.1141558.2557.-4183559.560.1152562.7561.713563.564.1111 1565.9566.61531568.567.212517569.570.15253571.4 x1x4572.573.y3y110xx67574.575.y43y7x2x4576.577.y1y11ax52579.578.y21b3x2x11580.581.y2y19x1x4582.7583.yy3329x22x3585.584.75y1y221x2x8586.587.3y28y2x7x370588.589.y0y1103349xx1023590.591.4916yy1023 9xx25592.593.y93y5x6x2594.595.y9y1x7x1597.596.y1y1x35x2599.598.y14y0.4x18x2601.600.19y6y2x5x1602.2603.yy135x1x605.604.2y1y1x2x5606.607.y1y7x2x3608.609.y2y8x5x4610.611.y16y2x2x5612.613.y1y7 x3x5614.1615.yy33x4x3616.617.y1y2x2x0618.619.y2y51xx4621.2620.y5y1 622.x1623.x2624.x5523625.x626.x1627.x779630.x4628.x629.x32631.x17632.x0633.x1715635.x3634.x16636.x710131638.x3639.x637.x97640.x2641.x4642.x2643.x4644.x3645.x320646.x4647.x1648.x39649.x6650.x2651.x25653.x82652.x654.x755655.x656.x7657.x334659.x6660.x3658.x291661.x5662.x2663.x271665.x1664.x666.x271667.x13668.x2669.x2 12672.x2670.x671.x95116673.x674.x675.x3435676.x2677.x10678.x411679.x1680.x3681.x77683.x1684.x1682.x525687.x2685.x4686.x2355689.x690.x8688.x421619691.x692.x3693.x75 1694.x5695.x3696.11x33697.x2698.14x699.21x2700.28x701.23x702.x22703.x704.x3705.21x35706.x4707.x6708.x121709.21x710.x711.x121712.2x713.31x714.无解2715.12x716.x1717.x2718.26x719.42x720.无解721.x4722.12x723.6x131724.x1725.2x726.无解25727.-1x2728.x729.x12730.x2731.42x732.12x7733.x2734.-1x735.x3413736.4x11737.x738.无解2279739.x1740.x2741.x125
简介：41.-5852.-845993.-1054.65.0.4146.277.-108.259.910.13.3411.-22712.-413.31.514.415.17516.251217.718.3119.8320.4.7321.501422.323.4.2224.2725.626.503 27.63128.1511129.4110230.11331.154000532.6733.1181034.4134535.436.2537.1138.11339.640.5241.042.6143.644.92445.3200246.2147.4 148.62149.57250.451.052.453.2054.30255.4356.757.1060158.259.1060.27161.6162.28163.16164.85365.2066.26167.168.812369.9670.4 571.272.511173.2259974.100175.276.877.13178.24579.280.45181.28482.2783.5584.285.786.1587.4888.689.8390.291.4192.2593.294.10095.696.250 297.998.5.0399.0100.899.5 101.1.995102.-40103.35.364104.-45105.199.51106.-156107.12452004108.-20042005109.-48110.31111.-31112.75113.425114.-2431115.-42116.-1516117.15118.5119.49 8120.542121.253122.8123.6124.0125.645126.24127.486128.0.8527129.16130.2961131.1827132.2133.3134.144135.1539136.20137.80138.71139.57140.3 14141.-91142.-3143.260144.25802007145.20072008146.26762147.3148.3149.0150.3.361151.-7152.73153.343154.57514155.1529156.236157.0.43158.-641159.103160.43.6161.94 1162.113163.1164.24.57165.4550166.77231167.31482168.631169.43170.15171.01172.2635173.361174.215175.21176.4177.-2178.-1179.0180.-4.48181.261182.10.08 183.3.47184.8.751185.4186.463187.5188.113189.121190.116191.90192.-181193.5194.0195.-235196.481197.315198.-8199.-45200.28 9201.7202.612203.71204.-7205.25206.31.3207.1201208.127209.6210.99211.161212.6213.113214.2025215.0216.903217.4218.123219.2220.851221.22 222.8223.229224.16125225.64226.31227.01228.55229.20230.27231.6232.10233.11234.4235.14236.121237.7235238.124239.3240.717241.2242.24243.501244.2245.11.04246.7 247.5248.10249.10601250.83251.1252.614253.27254.138255.89256.-2257.0258.14259.851260.1753261.43262.23263.64264.4265.251266.61267.22169268.196269.58 270.9056271.15272.31273.24125274.643275.50276.31277.48278.7227279.24280.25281.161282.25283.85284.11285.10286.22108287.7288.3421289.5290.0291.0292.0293.999216294.3 1295.81296.22297.0298.30.3299.2300.20 301.43302.11303.1.03304.8305.50306.8.5307.661308.3309.35310.6999311.19995312.481313.315314.8315.45316.289317.7318.31.3319.120320.903321.41322.125323.6324.99325.16 1326.613327.2025328.029329.6330.8.53331.4332.1333.7334.3335.7336.07337.16338.0339.81340.-434341.4191342.32343.91344.82345.25346.38.1347.1.5 1348.600349.0.320350.31351.8561352.6353.611354.225334355.3356.1.022357.43358.2359.1360.10361.9.7688362.315363.05364.72365.13319993366.111367.16368.51369.34 11370.91371.21372.565844373.43374.-104.727375.900376.199000377.0378.1379.05380.2125381.204382.125383.36189384.820073-3385.2386.0387.389732611388.20200389.101390.2 391.24755392.4393.482394.253395.12516396.2397.0125398.3399.03400.8 401.25402.9.5403.30404.13405.9406.172912407.408.2409.24331410.10411.5412.1321517413.17414.415.5241416.9417.418.121419.1420.58421.368191422.423.32.8424.496425.34426.50427.3085428.1429.14.5430.111315431.72432.433.448459434.435.3436.86502437.1438.24439.1005999765440.441.442.20097671444.200443.15445.121015021446.447.12448.1510132 142449.450.28451.295 1111452.原式1121231234123456722212334781111111222334781721841453.1011111454.原式25588111114141711111111111325588111114141711153217341111111455.原式41335355720012003200320051111004003413200320051204804579161182901111456.原式1133557791331.2540.83714611111111233579131234631823=244293611111457.原式1232026122042011111210122334452021111111121012233420211202101210212111111458.原式200820092010201120123669912121515181111111201059122356510050541325375117459.原式26153577有理数计算1 学而思初中优秀教学体系1111111112233557711110111111111111460.原式13355779911111313151111111112132352131511172115151111461.原式1111261299001119912239910011111991223991001991100198100111111111462.原式2122323346778788911121289351444949463.1980038625464.3400323200465.9603100100100100111466.原式…(…)1232343459910010123341001011111151100()()24221010021011011111111467.原式312323423434578989101111193123891021601111111468.原式3[(…)]312323423434517181918192011319201113912318192018192068403234316469.原式1232348910有理数计算2 学而思初中优秀教学体系111128321232348910123234891011111111113221223233489910233491031111111122129102334910311117112322290210460515571719470.23434589109101123349102343459101111111134244535101191111111134451011243591111111111111111111344510112243546810911111111181283131122103113325335531所以原式1155651．55222234512471.原式1234523456345671011121314154264374101441234523456345671011121314111123434545611121344441234523456345671011121314111111122334344511121213111111123423452345345610111213111213141111122312131234111213141111177111122121324111213148111213148211141175830861612349472.原式22323423452341021314110122323423410111111112223232342349234910有理数计算3 学而思初中优秀教学体系136287991234910362880013141516171473.原式12123123412345123456123456711111112121231231234123456711112121234567150391504050402399474.原式1231234123100314110011231234123100111111121231231234123991231001111121231002100!234550475.原式＝＋＋＋＋…＋1336610101512251275111111111274＝（）＋（）＋（）＋（）＝1336610122512751275211311476.，，……，1(12)112(12)(123)1212310011，所以(1299)(12100)1299121001原式1121001504915050505023410477.原式1()13366104555111111111336610455511115555111111478.原式()()()()()()244668810101212141111111111111()2446688101012121421113()2142141111311124479.1(1)(1)，1(1)(1)，……所以，2222222333331324485015025原式22334949249492222222221324387480.原式2222222212233478有理数计算4 学而思初中优秀教学体系11111111222222222334781631286422222481.原式1111122222315171199311995122299724461994199611111199724461994199611997997997219961996222222131024203534104204344482.，，，……由于2，2，2，2222133184115338815154444可见原式222222222131419911111298413243598100111111111964123243598100111196212991001991963299004751198495022221246100483.原式222242141611001111111111222242141611001111115041335579910111111111150142335579910111115063501501242101410110156677889910111111113484.()…()5667788991056679105101036233445566736111111485.原式=…=4572334455667572334671325711111121486.原式11111534578453738571231111112113487.原式357344547566711112123131113333665557774444有理数计算5 学而思初中优秀教学体系111111111111111488.原式23303141317717430341431111111112233743475791113153489.原式71861220304256811111111782334788111178828821111023344556677889910490.原式12334455667788991011111111111111111()()()()()()()()2334455667788991011312105111111112111491.原式45344535564611112452334561232341918192021919492.原式…2173621234318192019120202008111200711493.原式=(…)(…)2008120072200620071200812006200612008111200711=(…)(…)2008120072200620071200812006200611200820082008120072007=(…)(…)20081200722006200712008120062006111111111111=[(…)(…)]2008120072200620071120062006111111111111=[(…)(…)]200812007220062007112006200611111=()2008200720072015028111111111494.原式249835995152991111111112245035495254981111111112450354926274911111111112242435252628485011111111112424352513142450111111111112241235111416245025有理数计算6 学而思初中优秀教学体系1111111111124123511781250251111111111224635810125025111111111124635456502511491502550315171131495.原式335357357911131111111335357911335357911131135791113135134135135341199222224422496.135357171921133535571719192189224221335571719192188912222422所以原式1335171913355717191921921512133379192113399399497.2498.-3499.-3500.-17有理数计算7 8501.2502.131503.1504.2505.1506.911507.508.1148510.3509.7511.-1512.5513.5514.125515.516.91224517.518.817519.3520.19521.1522.416523.8524.344525.526.335552528.527.18515529.无解530.5617531.29532.25533.8534.3 17535.2536.2517537.5538.634539.1540.19541.3542.112543.1544.561545.546.772547.17548.5549.11550.03552.2551.5691553.554.23107555.556.1141558.2557.-4183559.560.1152562.7561.713563.564.1111 1565.9566.61531568.567.212517569.570.15253571.4 x1x4572.573.y3y110xx67574.575.y43y7x2x4576.577.y1y11ax52579.578.y21b3x2x11580.581.y2y19x1x4582.7583.yy3329x22x3585.584.75y1y221x2x8586.587.3y28y2x7x370588.589.y0y1103349xx1023590.591.4916yy1023 9xx25592.593.y93y5x6x2594.595.y9y1x7x1597.596.y1y1x35x2599.598.y14y0.4x18x2601.600.19y6y2x5x1602.2603.yy135x1x605.604.2y1y1x2x5606.607.y1y7x2x3608.609.y2y8x5x4610.611.y16y2x2x5612.613.y1y7 x3x5614.1615.yy33x4x3616.617.y1y2x2x0618.619.y2y51xx4621.2620.y5y1 622.x1623.x2624.x5523625.x626.x1627.x779630.x4628.x629.x32631.x17632.x0633.x1715635.x3634.x16636.x710131638.x3639.x637.x97640.x2641.x4642.x2643.x4644.x3645.x320646.x4647.x1648.x39649.x6650.x2651.x25653.x82652.x654.x755655.x656.x7657.x334659.x6660.x3658.x291661.x5662.x2663.x271665.x1664.x666.x271667.x13668.x2669.x2 12672.x2670.x671.x95116673.x674.x675.x3435676.x2677.x10678.x411679.x1680.x3681.x77683.x1684.x1682.x525687.x2685.x4686.x2355689.x690.x8688.x421619691.x692.x3693.x75 1694.x5695.x3696.11x33697.x2698.14x699.21x2700.28x701.23x702.x22703.x704.x3705.21x35706.x4707.x6708.x121709.21x710.x711.x121712.2x713.31x714.无解2715.12x716.x1717.x2718.26x719.42x720.无解721.x4722.12x723.6x131724.x1725.2x726.无解25727.-1x2728.x729.x12730.x2731.42x732.12x7733.x2734.-1x735.x3413736.4x11737.x738.无解2279739.x1740.x2741.x125
简介：41.-5852.-845993.-1054.65.0.4146.277.-108.259.910.13.3411.-22712.-413.31.514.415.17516.251217.718.3119.8320.4.7321.501422.323.4.2224.2725.626.503 27.63128.1511129.4110230.11331.154000532.6733.1181034.4134535.436.2537.1138.11339.640.5241.042.6143.644.92445.3200246.2147.4 148.62149.57250.451.052.453.2054.30255.4356.757.1060158.259.1060.27161.6162.28163.16164.85365.2066.26167.168.812369.9670.4 571.272.511173.2259974.100175.276.877.13178.24579.280.45181.28482.2783.5584.285.786.1587.4888.689.8390.291.4192.2593.294.10095.696.250 297.998.5.0399.0100.899.5 101.1.995102.-40103.35.364104.-45105.199.51106.-156107.12452004108.-20042005109.-48110.31111.-31112.75113.425114.-2431115.-42116.-1516117.15118.5119.49 8120.542121.253122.8123.6124.0125.645126.24127.486128.0.8527129.16130.2961131.1827132.2133.3134.144135.1539136.20137.80138.71139.57140.3 14141.-91142.-3143.260144.25802007145.20072008146.26762147.3148.3149.0150.3.361151.-7152.73153.343154.57514155.1529156.236157.0.43158.-641159.103160.43.6161.94 1162.113163.1164.24.57165.4550166.77231167.31482168.631169.43170.15171.01172.2635173.361174.215175.21176.4177.-2178.-1179.0180.-4.48181.261182.10.08 183.3.47184.8.751185.4186.463187.5188.113189.121190.116191.90192.-181193.5194.0195.-235196.481197.315198.-8199.-45200.28 9201.7202.612203.71204.-7205.25206.31.3207.1201208.127209.6210.99211.161212.6213.113214.2025215.0216.903217.4218.123219.2220.851221.22 222.8223.229224.16125225.64226.31227.01228.55229.20230.27231.6232.10233.11234.4235.14236.121237.7235238.124239.3240.717241.2242.24243.501244.2245.11.04246.7 247.5248.10249.10601250.83251.1252.614253.27254.138255.89256.-2257.0258.14259.851260.1753261.43262.23263.64264.4265.251266.61267.22169268.196269.58 270.9056271.15272.31273.24125274.643275.50276.31277.48278.7227279.24280.25281.161282.25283.85284.11285.10286.22108287.7288.3421289.5290.0291.0292.0293.999216294.3 1295.81296.22297.0298.30.3299.2300.20 301.43302.11303.1.03304.8305.50306.8.5307.661308.3309.35310.6999311.19995312.481313.315314.8315.45316.289317.7318.31.3319.120320.903321.41322.125323.6324.99325.16 1326.613327.2025328.029329.6330.8.53331.4332.1333.7334.3335.7336.07337.16338.0339.81340.-434341.4191342.32343.91344.82345.25346.38.1347.1.5 1348.600349.0.320350.31351.8561352.6353.611354.225334355.3356.1.022357.43358.2359.1360.10361.9.7688362.315363.05364.72365.13319993366.111367.16368.51369.34 11370.91371.21372.565844373.43374.-104.727375.900376.199000377.0378.1379.05380.2125381.204382.125383.36189384.820073-3385.2386.0387.389732611388.20200389.101390.2 391.24755392.4393.482394.253395.12516396.2397.0125398.3399.03400.8 401.25402.9.5403.30404.13405.9406.172912407.408.2409.24331410.10411.5412.1321517413.17414.415.5241416.9417.418.121419.1420.58421.368191422.423.32.8424.496425.34426.50427.3085428.1429.14.5430.111315431.72432.433.448459434.435.3436.86502437.1438.24439.1005999765440.441.442.20097671444.200443.15445.121015021446.447.12448.1510132 142449.450.28451.295 1111452.原式1121231234123456722212334781111111222334781721841453.1011111454.原式25588111114141711111111111325588111114141711153217341111111455.原式41335355720012003200320051111004003413200320051204804579161182901111456.原式1133557791331.2540.83714611111111233579131234631823=244293611111457.原式1232026122042011111210122334452021111111121012233420211202101210212111111458.原式200820092010201120123669912121515181111111201059122356510050541325375117459.原式26153577有理数计算1 学而思初中优秀教学体系1111111112233557711110111111111111460.原式13355779911111313151111111112132352131511172115151111461.原式1111261299001119912239910011111991223991001991100198100111111111462.原式2122323346778788911121289351444949463.1980038625464.3400323200465.9603100100100100111466.原式…(…)1232343459910010123341001011111151100()()24221010021011011111111467.原式312323423434578989101111193123891021601111111468.原式3[(…)]312323423434517181918192011319201113912318192018192068403234316469.原式1232348910有理数计算2 学而思初中优秀教学体系111128321232348910123234891011111111113221223233489910233491031111111122129102334910311117112322290210460515571719470.23434589109101123349102343459101111111134244535101191111111134451011243591111111111111111111344510112243546810911111111181283131122103113325335531所以原式1155651．55222234512471.原式1234523456345671011121314154264374101441234523456345671011121314111123434545611121344441234523456345671011121314111111122334344511121213111111123423452345345610111213111213141111122312131234111213141111177111122121324111213148111213148211141175830861612349472.原式22323423452341021314110122323423410111111112223232342349234910有理数计算3 学而思初中优秀教学体系136287991234910362880013141516171473.原式12123123412345123456123456711111112121231231234123456711112121234567150391504050402399474.原式1231234123100314110011231234123100111111121231231234123991231001111121231002100!234550475.原式＝＋＋＋＋…＋1336610101512251275111111111274＝（）＋（）＋（）＋（）＝1336610122512751275211311476.，，……，1(12)112(12)(123)1212310011，所以(1299)(12100)1299121001原式1121001504915050505023410477.原式1()13366104555111111111336610455511115555111111478.原式()()()()()()244668810101212141111111111111()2446688101012121421113()2142141111311124479.1(1)(1)，1(1)(1)，……所以，2222222333331324485015025原式22334949249492222222221324387480.原式2222222212233478有理数计算4 学而思初中优秀教学体系11111111222222222334781631286422222481.原式1111122222315171199311995122299724461994199611111199724461994199611997997997219961996222222131024203534104204344482.，，，……由于2，2，2，2222133184115338815154444可见原式222222222131419911111298413243598100111111111964123243598100111196212991001991963299004751198495022221246100483.原式222242141611001111111111222242141611001111115041335579910111111111150142335579910111115063501501242101410110156677889910111111113484.()…()5667788991056679105101036233445566736111111485.原式=…=4572334455667572334671325711111121486.原式11111534578453738571231111112113487.原式357344547566711112123131113333665557774444有理数计算5 学而思初中优秀教学体系111111111111111488.原式23303141317717430341431111111112233743475791113153489.原式71861220304256811111111782334788111178828821111023344556677889910490.原式12334455667788991011111111111111111()()()()()()()()2334455667788991011312105111111112111491.原式45344535564611112452334561232341918192021919492.原式…2173621234318192019120202008111200711493.原式=(…)(…)2008120072200620071200812006200612008111200711=(…)(…)2008120072200620071200812006200611200820082008120072007=(…)(…)20081200722006200712008120062006111111111111=[(…)(…)]2008120072200620071120062006111111111111=[(…)(…)]200812007220062007112006200611111=()2008200720072015028111111111494.原式249835995152991111111112245035495254981111111112450354926274911111111112242435252628485011111111112424352513142450111111111112241235111416245025有理数计算6 学而思初中优秀教学体系1111111111124123511781250251111111111224635810125025111111111124635456502511491502550315171131495.原式335357357911131111111335357911335357911131135791113135134135135341199222224422496.135357171921133535571719192189224221335571719192188912222422所以原式1335171913355717191921921512133379192113399399497.2498.-3499.-3500.-17有理数计算7 8501.2502.131503.1504.2505.1506.911507.508.1148510.3509.7511.-1512.5513.5514.125515.516.91224517.518.817519.3520.19521.1522.416523.8524.344525.526.335552528.527.18515529.无解530.5617531.29532.25533.8534.3 17535.2536.2517537.5538.634539.1540.19541.3542.112543.1544.561545.546.772547.17548.5549.11550.03552.2551.5691553.554.23107555.556.1141558.2557.-4183559.560.1152562.7561.713563.564.1111 1565.9566.61531568.567.212517569.570.15253571.4 x1x4572.573.y3y110xx67574.575.y43y7x2x4576.577.y1y11ax52579.578.y21b3x2x11580.581.y2y19x1x4582.7583.yy3329x22x3585.584.75y1y221x2x8586.587.3y28y2x7x370588.589.y0y1103349xx1023590.591.4916yy1023 9xx25592.593.y93y5x6x2594.595.y9y1x7x1597.596.y1y1x35x2599.598.y14y0.4x18x2601.600.19y6y2x5x1602.2603.yy135x1x605.604.2y1y1x2x5606.607.y1y7x2x3608.609.y2y8x5x4610.611.y16y2x2x5612.613.y1y7 x3x5614.1615.yy33x4x3616.617.y1y2x2x0618.619.y2y51xx4621.2620.y5y1 622.x1623.x2624.x5523625.x626.x1627.x779630.x4628.x629.x32631.x17632.x0633.x1715635.x3634.x16636.x710131638.x3639.x637.x97640.x2641.x4642.x2643.x4644.x3645.x320646.x4647.x1648.x39649.x6650.x2651.x25653.x82652.x654.x755655.x656.x7657.x334659.x6660.x3658.x291661.x5662.x2663.x271665.x1664.x666.x271667.x13668.x2669.x2 12672.x2670.x671.x95116673.x674.x675.x3435676.x2677.x10678.x411679.x1680.x3681.x77683.x1684.x1682.x525687.x2685.x4686.x2355689.x690.x8688.x421619691.x692.x3693.x75 1694.x5695.x3696.11x33697.x2698.14x699.21x2700.28x701.23x702.x22703.x704.x3705.21x35706.x4707.x6708.x121709.21x710.x711.x121712.2x713.31x714.无解2715.12x716.x1717.x2718.26x719.42x720.无解721.x4722.12x723.6x131724.x1725.2x726.无解25727.-1x2728.x729.x12730.x2731.42x732.12x7733.x2734.-1x735.x3413736.4x11737.x738.无解2279739.x1740.x2741.x125
简介：41.-5852.-845993.-1054.65.0.4146.277.-108.259.910.13.3411.-22712.-413.31.514.415.17516.251217.718.3119.8320.4.7321.501422.323.4.2224.2725.626.503 27.63128.1511129.4110230.11331.154000532.6733.1181034.4134535.436.2537.1138.11339.640.5241.042.6143.644.92445.3200246.2147.4 148.62149.57250.451.052.453.2054.30255.4356.757.1060158.259.1060.27161.6162.28163.16164.85365.2066.26167.168.812369.9670.4 571.272.511173.2259974.100175.276.877.13178.24579.280.45181.28482.2783.5584.285.786.1587.4888.689.8390.291.4192.2593.294.10095.696.250 297.998.5.0399.0100.899.5 101.1.995102.-40103.35.364104.-45105.199.51106.-156107.12452004108.-20042005109.-48110.31111.-31112.75113.425114.-2431115.-42116.-1516117.15118.5119.49 8120.542121.253122.8123.6124.0125.645126.24127.486128.0.8527129.16130.2961131.1827132.2133.3134.144135.1539136.20137.80138.71139.57140.3 14141.-91142.-3143.260144.25802007145.20072008146.26762147.3148.3149.0150.3.361151.-7152.73153.343154.57514155.1529156.236157.0.43158.-641159.103160.43.6161.94 1162.113163.1164.24.57165.4550166.77231167.31482168.631169.43170.15171.01172.2635173.361174.215175.21176.4177.-2178.-1179.0180.-4.48181.261182.10.08 183.3.47184.8.751185.4186.463187.5188.113189.121190.116191.90192.-181193.5194.0195.-235196.481197.315198.-8199.-45200.28 9201.7202.612203.71204.-7205.25206.31.3207.1201208.127209.6210.99211.161212.6213.113214.2025215.0216.903217.4218.123219.2220.851221.22 222.8223.229224.16125225.64226.31227.01228.55229.20230.27231.6232.10233.11234.4235.14236.121237.7235238.124239.3240.717241.2242.24243.501244.2245.11.04246.7 247.5248.10249.10601250.83251.1252.614253.27254.138255.89256.-2257.0258.14259.851260.1753261.43262.23263.64264.4265.251266.61267.22169268.196269.58 270.9056271.15272.31273.24125274.643275.50276.31277.48278.7227279.24280.25281.161282.25283.85284.11285.10286.22108287.7288.3421289.5290.0291.0292.0293.999216294.3 1295.81296.22297.0298.30.3299.2300.20 301.43302.11303.1.03304.8305.50306.8.5307.661308.3309.35310.6999311.19995312.481313.315314.8315.45316.289317.7318.31.3319.120320.903321.41322.125323.6324.99325.16 1326.613327.2025328.029329.6330.8.53331.4332.1333.7334.3335.7336.07337.16338.0339.81340.-434341.4191342.32343.91344.82345.25346.38.1347.1.5 1348.600349.0.320350.31351.8561352.6353.611354.225334355.3356.1.022357.43358.2359.1360.10361.9.7688362.315363.05364.72365.13319993366.111367.16368.51369.34 11370.91371.21372.565844373.43374.-104.727375.900376.199000377.0378.1379.05380.2125381.204382.125383.36189384.820073-3385.2386.0387.389732611388.20200389.101390.2 391.24755392.4393.482394.253395.12516396.2397.0125398.3399.03400.8 401.25402.9.5403.30404.13405.9406.172912407.408.2409.24331410.10411.5412.1321517413.17414.415.5241416.9417.418.121419.1420.58421.368191422.423.32.8424.496425.34426.50427.3085428.1429.14.5430.111315431.72432.433.448459434.435.3436.86502437.1438.24439.1005999765440.441.442.20097671444.200443.15445.121015021446.447.12448.1510132 142449.450.28451.295 1111452.原式1121231234123456722212334781111111222334781721841453.1011111454.原式25588111114141711111111111325588111114141711153217341111111455.原式41335355720012003200320051111004003413200320051204804579161182901111456.原式1133557791331.2540.83714611111111233579131234631823=244293611111457.原式1232026122042011111210122334452021111111121012233420211202101210212111111458.原式200820092010201120123669912121515181111111201059122356510050541325375117459.原式26153577有理数计算1 学而思初中优秀教学体系1111111112233557711110111111111111460.原式13355779911111313151111111112132352131511172115151111461.原式1111261299001119912239910011111991223991001991100198100111111111462.原式2122323346778788911121289351444949463.1980038625464.3400323200465.9603100100100100111466.原式…(…)1232343459910010123341001011111151100()()24221010021011011111111467.原式312323423434578989101111193123891021601111111468.原式3[(…)]312323423434517181918192011319201113912318192018192068403234316469.原式1232348910有理数计算2 学而思初中优秀教学体系111128321232348910123234891011111111113221223233489910233491031111111122129102334910311117112322290210460515571719470.23434589109101123349102343459101111111134244535101191111111134451011243591111111111111111111344510112243546810911111111181283131122103113325335531所以原式1155651．55222234512471.原式1234523456345671011121314154264374101441234523456345671011121314111123434545611121344441234523456345671011121314111111122334344511121213111111123423452345345610111213111213141111122312131234111213141111177111122121324111213148111213148211141175830861612349472.原式22323423452341021314110122323423410111111112223232342349234910有理数计算3 学而思初中优秀教学体系136287991234910362880013141516171473.原式12123123412345123456123456711111112121231231234123456711112121234567150391504050402399474.原式1231234123100314110011231234123100111111121231231234123991231001111121231002100!234550475.原式＝＋＋＋＋…＋1336610101512251275111111111274＝（）＋（）＋（）＋（）＝1336610122512751275211311476.，，……，1(12)112(12)(123)1212310011，所以(1299)(12100)1299121001原式1121001504915050505023410477.原式1()13366104555111111111336610455511115555111111478.原式()()()()()()244668810101212141111111111111()2446688101012121421113()2142141111311124479.1(1)(1)，1(1)(1)，……所以，2222222333331324485015025原式22334949249492222222221324387480.原式2222222212233478有理数计算4 学而思初中优秀教学体系11111111222222222334781631286422222481.原式1111122222315171199311995122299724461994199611111199724461994199611997997997219961996222222131024203534104204344482.，，，……由于2，2，2，2222133184115338815154444可见原式222222222131419911111298413243598100111111111964123243598100111196212991001991963299004751198495022221246100483.原式222242141611001111111111222242141611001111115041335579910111111111150142335579910111115063501501242101410110156677889910111111113484.()…()5667788991056679105101036233445566736111111485.原式=…=4572334455667572334671325711111121486.原式11111534578453738571231111112113487.原式357344547566711112123131113333665557774444有理数计算5 学而思初中优秀教学体系111111111111111488.原式23303141317717430341431111111112233743475791113153489.原式71861220304256811111111782334788111178828821111023344556677889910490.原式12334455667788991011111111111111111()()()()()()()()2334455667788991011312105111111112111491.原式45344535564611112452334561232341918192021919492.原式…2173621234318192019120202008111200711493.原式=(…)(…)2008120072200620071200812006200612008111200711=(…)(…)2008120072200620071200812006200611200820082008120072007=(…)(…)20081200722006200712008120062006111111111111=[(…)(…)]2008120072200620071120062006111111111111=[(…)(…)]200812007220062007112006200611111=()2008200720072015028111111111494.原式249835995152991111111112245035495254981111111112450354926274911111111112242435252628485011111111112424352513142450111111111112241235111416245025有理数计算6 学而思初中优秀教学体系1111111111124123511781250251111111111224635810125025111111111124635456502511491502550315171131495.原式335357357911131111111335357911335357911131135791113135134135135341199222224422496.135357171921133535571719192189224221335571719192188912222422所以原式1335171913355717191921921512133379192113399399497.2498.-3499.-3500.-17有理数计算7 8501.2502.131503.1504.2505.1506.911507.508.1148510.3509.7511.-1512.5513.5514.125515.516.91224517.518.817519.3520.19521.1522.416523.8524.344525.526.335552528.527.18515529.无解530.5617531.29532.25533.8534.3 17535.2536.2517537.5538.634539.1540.19541.3542.112543.1544.561545.546.772547.17548.5549.11550.03552.2551.5691553.554.23107555.556.1141558.2557.-4183559.560.1152562.7561.713563.564.1111 1565.9566.61531568.567.212517569.570.15253571.4 x1x4572.573.y3y110xx67574.575.y43y7x2x4576.577.y1y11ax52579.578.y21b3x2x11580.581.y2y19x1x4582.7583.yy3329x22x3585.584.75y1y221x2x8586.587.3y28y2x7x370588.589.y0y1103349xx1023590.591.4916yy1023 9xx25592.593.y93y5x6x2594.595.y9y1x7x1597.596.y1y1x35x2599.598.y14y0.4x18x2601.600.19y6y2x5x1602.2603.yy135x1x605.604.2y1y1x2x5606.607.y1y7x2x3608.609.y2y8x5x4610.611.y16y2x2x5612.613.y1y7 x3x5614.1615.yy33x4x3616.617.y1y2x2x0618.619.y2y51xx4621.2620.y5y1 622.x1623.x2624.x5523625.x626.x1627.x779630.x4628.x629.x32631.x17632.x0633.x1715635.x3634.x16636.x710131638.x3639.x637.x97640.x2641.x4642.x2643.x4644.x3645.x320646.x4647.x1648.x39649.x6650.x2651.x25653.x82652.x654.x755655.x656.x7657.x334659.x6660.x3658.x291661.x5662.x2663.x271665.x1664.x666.x271667.x13668.x2669.x2 12672.x2670.x671.x95116673.x674.x675.x3435676.x2677.x10678.x411679.x1680.x3681.x77683.x1684.x1682.x525687.x2685.x4686.x2355689.x690.x8688.x421619691.x692.x3693.x75 1694.x5695.x3696.11x33697.x2698.14x699.21x2700.28x701.23x702.x22703.x704.x3705.21x35706.x4707.x6708.x121709.21x710.x711.x121712.2x713.31x714.无解2715.12x716.x1717.x2718.26x719.42x720.无解721.x4722.12x723.6x131724.x1725.2x726.无解25727.-1x2728.x729.x12730.x2731.42x732.12x7733.x2734.-1x735.x3413736.4x11737.x738.无解2279739.x1740.x2741.x125
简介：41.-5852.-845993.-1054.65.0.4146.277.-108.259.910.13.3411.-22712.-413.31.514.415.17516.251217.718.3119.8320.4.7321.501422.323.4.2224.2725.626.503 27.63128.1511129.4110230.11331.154000532.6733.1181034.4134535.436.2537.1138.11339.640.5241.042.6143.644.92445.3200246.2147.4 148.62149.57250.451.052.453.2054.30255.4356.757.1060158.259.1060.27161.6162.28163.16164.85365.2066.26167.168.812369.9670.4 571.272.511173.2259974.100175.276.877.13178.24579.280.45181.28482.2783.5584.285.786.1587.4888.689.8390.291.4192.2593.294.10095.696.250 297.998.5.0399.0100.899.5 101.1.995102.-40103.35.364104.-45105.199.51106.-156107.12452004108.-20042005109.-48110.31111.-31112.75113.425114.-2431115.-42116.-1516117.15118.5119.49 8120.542121.253122.8123.6124.0125.645126.24127.486128.0.8527129.16130.2961131.1827132.2133.3134.144135.1539136.20137.80138.71139.57140.3 14141.-91142.-3143.260144.25802007145.20072008146.26762147.3148.3149.0150.3.361151.-7152.73153.343154.57514155.1529156.236157.0.43158.-641159.103160.43.6161.94 1162.113163.1164.24.57165.4550166.77231167.31482168.631169.43170.15171.01172.2635173.361174.215175.21176.4177.-2178.-1179.0180.-4.48181.261182.10.08 183.3.47184.8.751185.4186.463187.5188.113189.121190.116191.90192.-181193.5194.0195.-235196.481197.315198.-8199.-45200.28 9201.7202.612203.71204.-7205.25206.31.3207.1201208.127209.6210.99211.161212.6213.113214.2025215.0216.903217.4218.123219.2220.851221.22 222.8223.229224.16125225.64226.31227.01228.55229.20230.27231.6232.10233.11234.4235.14236.121237.7235238.124239.3240.717241.2242.24243.501244.2245.11.04246.7 247.5248.10249.10601250.83251.1252.614253.27254.138255.89256.-2257.0258.14259.851260.1753261.43262.23263.64264.4265.251266.61267.22169268.196269.58 270.9056271.15272.31273.24125274.643275.50276.31277.48278.7227279.24280.25281.161282.25283.85284.11285.10286.22108287.7288.3421289.5290.0291.0292.0293.999216294.3 1295.81296.22297.0298.30.3299.2300.20 301.43302.11303.1.03304.8305.50306.8.5307.661308.3309.35310.6999311.19995312.481313.315314.8315.45316.289317.7318.31.3319.120320.903321.41322.125323.6324.99325.16 1326.613327.2025328.029329.6330.8.53331.4332.1333.7334.3335.7336.07337.16338.0339.81340.-434341.4191342.32343.91344.82345.25346.38.1347.1.5 1348.600349.0.320350.31351.8561352.6353.611354.225334355.3356.1.022357.43358.2359.1360.10361.9.7688362.315363.05364.72365.13319993366.111367.16368.51369.34 11370.91371.21372.565844373.43374.-104.727375.900376.199000377.0378.1379.05380.2125381.204382.125383.36189384.820073-3385.2386.0387.389732611388.20200389.101390.2 391.24755392.4393.482394.253395.12516396.2397.0125398.3399.03400.8 401.25402.9.5403.30404.13405.9406.172912407.408.2409.24331410.10411.5412.1321517413.17414.415.5241416.9417.418.121419.1420.58421.368191422.423.32.8424.496425.34426.50427.3085428.1429.14.5430.111315431.72432.433.448459434.435.3436.86502437.1438.24439.1005999765440.441.442.20097671444.200443.15445.121015021446.447.12448.1510132 142449.450.28451.295 1111452.原式1121231234123456722212334781111111222334781721841453.1011111454.原式25588111114141711111111111325588111114141711153217341111111455.原式41335355720012003200320051111004003413200320051204804579161182901111456.原式1133557791331.2540.83714611111111233579131234631823=244293611111457.原式1232026122042011111210122334452021111111121012233420211202101210212111111458.原式200820092010201120123669912121515181111111201059122356510050541325375117459.原式26153577有理数计算1 学而思初中优秀教学体系1111111112233557711110111111111111460.原式13355779911111313151111111112132352131511172115151111461.原式1111261299001119912239910011111991223991001991100198100111111111462.原式2122323346778788911121289351444949463.1980038625464.3400323200465.9603100100100100111466.原式…(…)1232343459910010123341001011111151100()()24221010021011011111111467.原式312323423434578989101111193123891021601111111468.原式3[(…)]312323423434517181918192011319201113912318192018192068403234316469.原式1232348910有理数计算2 学而思初中优秀教学体系111128321232348910123234891011111111113221223233489910233491031111111122129102334910311117112322290210460515571719470.23434589109101123349102343459101111111134244535101191111111134451011243591111111111111111111344510112243546810911111111181283131122103113325335531所以原式1155651．55222234512471.原式1234523456345671011121314154264374101441234523456345671011121314111123434545611121344441234523456345671011121314111111122334344511121213111111123423452345345610111213111213141111122312131234111213141111177111122121324111213148111213148211141175830861612349472.原式22323423452341021314110122323423410111111112223232342349234910有理数计算3 学而思初中优秀教学体系136287991234910362880013141516171473.原式12123123412345123456123456711111112121231231234123456711112121234567150391504050402399474.原式1231234123100314110011231234123100111111121231231234123991231001111121231002100!234550475.原式＝＋＋＋＋…＋1336610101512251275111111111274＝（）＋（）＋（）＋（）＝1336610122512751275211311476.，，……，1(12)112(12)(123)1212310011，所以(1299)(12100)1299121001原式1121001504915050505023410477.原式1()13366104555111111111336610455511115555111111478.原式()()()()()()244668810101212141111111111111()2446688101012121421113()2142141111311124479.1(1)(1)，1(1)(1)，……所以，2222222333331324485015025原式22334949249492222222221324387480.原式2222222212233478有理数计算4 学而思初中优秀教学体系11111111222222222334781631286422222481.原式1111122222315171199311995122299724461994199611111199724461994199611997997997219961996222222131024203534104204344482.，，，……由于2，2，2，2222133184115338815154444可见原式222222222131419911111298413243598100111111111964123243598100111196212991001991963299004751198495022221246100483.原式222242141611001111111111222242141611001111115041335579910111111111150142335579910111115063501501242101410110156677889910111111113484.()…()5667788991056679105101036233445566736111111485.原式=…=4572334455667572334671325711111121486.原式11111534578453738571231111112113487.原式357344547566711112123131113333665557774444有理数计算5 学而思初中优秀教学体系111111111111111488.原式23303141317717430341431111111112233743475791113153489.原式71861220304256811111111782334788111178828821111023344556677889910490.原式12334455667788991011111111111111111()()()()()()()()2334455667788991011312105111111112111491.原式45344535564611112452334561232341918192021919492.原式…2173621234318192019120202008111200711493.原式=(…)(…)2008120072200620071200812006200612008111200711=(…)(…)2008120072200620071200812006200611200820082008120072007=(…)(…)20081200722006200712008120062006111111111111=[(…)(…)]2008120072200620071120062006111111111111=[(…)(…)]200812007220062007112006200611111=()2008200720072015028111111111494.原式249835995152991111111112245035495254981111111112450354926274911111111112242435252628485011111111112424352513142450111111111112241235111416245025有理数计算6 学而思初中优秀教学体系1111111111124123511781250251111111111224635810125025111111111124635456502511491502550315171131495.原式335357357911131111111335357911335357911131135791113135134135135341199222224422496.135357171921133535571719192189224221335571719192188912222422所以原式1335171913355717191921921512133379192113399399497.2498.-3499.-3500.-17有理数计算7 8501.2502.131503.1504.2505.1506.911507.508.1148510.3509.7511.-1512.5513.5514.125515.516.91224517.518.817519.3520.19521.1522.416523.8524.344525.526.335552528.527.18515529.无解530.5617531.29532.25533.8534.3 17535.2536.2517537.5538.634539.1540.19541.3542.112543.1544.561545.546.772547.17548.5549.11550.03552.2551.5691553.554.23107555.556.1141558.2557.-4183559.560.1152562.7561.713563.564.1111 1565.9566.61531568.567.212517569.570.15253571.4 x1x4572.573.y3y110xx67574.575.y43y7x2x4576.577.y1y11ax52579.578.y21b3x2x11580.581.y2y19x1x4582.7583.yy3329x22x3585.584.75y1y221x2x8586.587.3y28y2x7x370588.589.y0y1103349xx1023590.591.4916yy1023 9xx25592.593.y93y5x6x2594.595.y9y1x7x1597.596.y1y1x35x2599.598.y14y0.4x18x2601.600.19y6y2x5x1602.2603.yy135x1x605.604.2y1y1x2x5606.607.y1y7x2x3608.609.y2y8x5x4610.611.y16y2x2x5612.613.y1y7 x3x5614.1615.yy33x4x3616.617.y1y2x2x0618.619.y2y51xx4621.2620.y5y1 622.x1623.x2624.x5523625.x626.x1627.x779630.x4628.x629.x32631.x17632.x0633.x1715635.x3634.x16636.x710131638.x3639.x637.x97640.x2641.x4642.x2643.x4644.x3645.x320646.x4647.x1648.x39649.x6650.x2651.x25653.x82652.x654.x755655.x656.x7657.x334659.x6660.x3658.x291661.x5662.x2663.x271665.x1664.x666.x271667.x13668.x2669.x2 12672.x2670.x671.x95116673.x674.x675.x3435676.x2677.x10678.x411679.x1680.x3681.x77683.x1684.x1682.x525687.x2685.x4686.x2355689.x690.x8688.x421619691.x692.x3693.x75 1694.x5695.x3696.11x33697.x2698.14x699.21x2700.28x701.23x702.x22703.x704.x3705.21x35706.x4707.x6708.x121709.21x710.x711.x121712.2x713.31x714.无解2715.12x716.x1717.x2718.26x719.42x720.无解721.x4722.12x723.6x131724.x1725.2x726.无解25727.-1x2728.x729.x12730.x2731.42x732.12x7733.x2734.-1x735.x3413736.4x11737.x738.无解2279739.x1740.x2741.x125