Question

求数列{(2n+1)/【n的平方*(n+1)的平方】}的前n项和

Answer 1

(2n+1)/[n^2(n+1)^2]

=1/n^2-1/(n+1)^2

sn=1/1^2-1/2^2+1/2^2-1/3^2+1/3^2-1/4^2+.+1/n^2-1/(n+1)^2

=1-1/(n+1)^2

=(n^2+2n)/(n+1)^2