一道六年级简算题 (1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/…(1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/100)·(1/2+1/3+1/4+……+1/99)

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一道六年级简算题(1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/…(1+1/2+1/3+1/4+……+1/99)·

一道六年级简算题 (1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/…(1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/100)·(1/2+1/3+1/4+……+1/99)
一道六年级简算题 (1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/…

(1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/100)·(1/2+1/3+1/4+……+1/99) 

一道六年级简算题 (1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/…(1+1/2+1/3+1/4+……+1/99)·(1/2+1/3+1/4+……+1/100)-(1+1/2+1/3+1/4+……+1/100)·(1/2+1/3+1/4+……+1/99)
这个题目的关键是整体思想

设1/2+1/3+1/4+……+1/99=a
则原式可化为
(1+a)(a+1/100)-(1+a+1/100)a
=a+1/100+a²+a/100-a-a²-a/100
=1/100