计算：1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)

分类: 作业答案 • 2022-05-27 15:11:02

问题描述：

计算：1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)
快啊,等着救命聂!

答

裂项：1/a(a+1)=1/a-1/(a+1)
1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2006)-1/(a+2007)
=1/a-1/(a+2007)