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求1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)的简便算法
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人气:368 ℃ 时间:2019-12-06 16:52:58
解答
1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)
=1/4(1/1*3-1/3*5)+1/4(1/3*5-1/5*7)+1/4(1/5*7-1/7*9)+1/4(1/7*9-1/9*11)
=1/4×1/1*3 - 1/4×1/9*11
=8/99
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