计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]

分类: 作业答案 • 2021-12-19 17:36:57

问题描述：

答

1/a(a+1)+.......=1/a-1/(a+1)+1/(a+1)-1/(a+2)+......+1/(a+2003)-1/(a+2004)=1/a-1/(a+2004)=2004/a(a+2004)

答

原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)……+1/(a+2003)-1/(a+2004)
=1/a-1/(a+2004)
=2004/a(a+2004)