求数列3/1*(2^2),5/(2^2)*(3^2),7/(3^2)*(4^2),……,(2n+1)/a^2(n+1)^2的前n项_数学解答

求数列3/1*(2^2),5/(2^2)*(3^2),7/(3^2)*(4^2),……,(2n+1)/a^2(n+1)^2的前n项和

人气：451 ℃　时间：2020-04-04 15:04:05

解答

(2n+1)/n^2(n+1)^2 = 1/n^2 - 1/(n+1)^2
SUM(3/1*(2^2),5/(2^2)*(3^2),7/(3^2)*(4^2),……,(2n+1)/a^2(n+1)^2)
=(1/1-1/2^2)+(1/2^2-1/3^2)+(1/3^2-1/4^2)+.+(1/n^2-1/(n+1)^2)
=1-1/(n+1)^2