数列1/(2n-1)(2n 3)怎么求和

题目

数列1/(2n-1)(2n 3)怎么求和

答案

an=1/(2n-1)(2n+3)=[1/(2n-1)-1/(2n+3)]/4
所以Sn=[(1-1/5)+(1/3-1/7)+(1/5-1/9)+...+(1/(2n-1)-1/(2n+3))]/4
=[1+1/3-1/(2n+1)-1/(2n+3)]/4
=1/3-(n+1)/[(2n+1)(2n+3)]