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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
分數連乘（急）大師請進
Oct 7th 2013, 10:32

用拆項對消

舉例來說:1/n×1/(n+1)=1/n-1/(n+1)

以此類推

1×1/2＋1/2×1/3＋1/3×1/4＋……＋1/9×1/10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
+(1/9-1/10)
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+(-1/6+1/6)+(-1/7+1/7)+(-1/8+1/8)
+(-1/9+1/9)-1/10
=1+0+0+0+0+0+0+0+0-1/10
=1-1/10
=9/10

Ans:10分之9

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