设an=(1/n+1)+(1/n+2)+(1/n+3)+...+1/2n,则an+1-an等于?
问题描述：
设an=(1/n+1)+(1/n+2)+(1/n+3)+...+1/2n,则an+1-an等于?
答
An=1/(n+1)+1/(n+2)+…+1/(2n-1)+1/(2n) 则An+1=1/(n+2)+1/(n+3)+…+1/(2n-1)+1/(2n)+ 1/(2n+1)+1/(2n+2)则An+1-An=1/(2n+1)+1/(2n+2)-1/(n+1)=1/(2n+1)-1/(2n+2)=1/[(2n+1)(2n+2)]