分式的加减法习题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)

分类: 作业答案 • 2021-12-20 12:24:26

问题描述：

分式的加减法习题
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)

答

1/a(a+1)=1/a-1/(a+1)
所以原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2006)-1/(a+2007)
=1/a-1/(a+2007)
=2007/a(a+2007)