1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=?

zhujiawen8882022-10-04 11:39:542条回答

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zsxlct 共回答了18个问题 | 采纳率88.9%: ∵2*【1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102】
=1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/99-1/101+1/100-1/102
=1+1/2-1/101-1/102
=(101*102+101*51-102-101)/101*102
=15250/10302
=7625/5151
∴ 1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=12=7625/10302; 1年前

jojonew 共回答了7962个问题 | 采纳率: 1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102
=（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/100-1/102）÷2
=（1+1/2-1/101-1/102）÷2
=15250/10302÷2
=7625/5151; 1年前

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1/2x4十1/4x6十…十1/100X102 meigz1年前1: flb001 共回答了19个问题 | 采纳率89.5%

1/2x4=1/2(1/2-1/4)
1/4x6=1/2(1/4-1/6)
以此类推
1/100X102=1/2（1/100-1/102）
所以
1/2x4十1/4x6十…十1/100X102
=1/2(1/2-1/4)+1/2(1/4-1/6)十…十1/2(1/100-1/102)
=1/2(1/2-1/102)
=25/102

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