求数列{(n+1)²+1/(n+1)²-1}的前n项和

求数列{(n+1)²+1/(n+1)²-1}的前n项和
求数列{(n+1)²+1/(n+1)²-1}的前n项和

求数列{(n+1)²+1/(n+1)²-1}的前n项和
an =[(n+1)^2+ 1]/[(n+1)^2 -1]
= 1 + 2/[(n+1)^2 -1]
= 1+ 2/[n(n+2)]
= 1+ [1/n - 1/(n+2) ]
Sn = a1+a2+...+an
= n + [ 1+ 1/2 - 1/(n+1) -1/(n+2) ]
= n + 3/2 - 1/(n+1) -1/(n+2)