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)

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/29 10:46:27

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