一乘二分之一加二乘三分之一加三乘四分之一……加三十九乘四十分之一
人气：133 ℃ 时间：2019-10-19 20:41:17
解答
1/(1×2）=1-1/2
1/(2×3）=1/2-1/3
1/(3×4）=1/3-1/4
1/(4×5）=1/4-1/5
...
1/(39×40）=1/39-1/40
左边相加=右边相加=1-1/40=39/40
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