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+200_数学解答

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)

人气：295 ℃　时间：2020-03-25 09:27:15

解答

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)