An=1/(n+1)+1/(n+2)+.+1/2n,则An+1-An等于?An+1中n＋1为下标_数学解答

An=1/(n+1)+1/(n+2)+.+1/2n,则An+1-An等于?
An+1中n＋1为下标

人气：249 ℃　时间：2019-11-12 01:24:09

解答

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)]