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
问题描述：
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
答
将通项（2n+1)/a^2(n+1)^2裂开即（2n+1)/a^2(n+1)^2=1/n~2 -1/(n+1)~2前后消去只剩1-1/(n+1)~2即可
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