1/1x5+1/5x9+1/9x13+……+1/25x29

分类: 作业答案 • 2023-01-09 12:10:12

问题描述：

答

1/(1×5)+1/(5×9)+...+1/(25×29)
=(1/4)(1-1/5+1/5-1/9+...+1/25-1/29)
=(1/4)(1-1/29)
=(1/4)(28/29)
=7/29
一般的对于正整数n,k
1/[n(n+k)]=(1/k)[1/n -1/(n+k)]