|1/3-1/2|+|1/4-1/3|+|1/6-1/5|+...+|1/10-1/9|的值
来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 09:42:18
|1/3-1/2|+|1/4-1/3|+|1/6-1/5|+...+|1/10-1/9|的值|1/3-1/2|+|1/4-1/3|+|1/6-1/5|+...+|1/10-1/9|的值|1/3-1/2
|1/3-1/2|+|1/4-1/3|+|1/6-1/5|+...+|1/10-1/9|的值
|1/3-1/2|+|1/4-1/3|+|1/6-1/5|+...+|1/10-1/9|的值
|1/3-1/2|+|1/4-1/3|+|1/6-1/5|+...+|1/10-1/9|的值
你是不是少输了一项,原题是不是:
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9|
=1/2-1/3+1/3-1/4+1/4-1/5...+1/9-1/10
=1/2-1/10
=2/5
因为 1/2 > 1/3 > 1/4 > 1/5 > 1/6 > 1/7 > 1/8 > 1/9 > 1/10
所以原式=-(1/3-1/2)-(1/4-1/3)-(1/6-1/5)-...-(1/10-1/9)
=1/2-1/3+1/3-1/4+1/4.......+1/9-1/10
=1/2-1/10
=2/5
直接展开
1/2-1/3+1/3-1/4+1/4.......+1/9-1/10
=1/2-1/10
=2/5