求数列2²+1/2²-1,3²+1/3²-1,.,（n+1）²+1/（n-1）²-1的前n项和Sn

求数列2²+1/2²-1,3²+1/3²-1,.,（n+1）²+1/（n-1）²-1的前n项和Sn
求数列2²+1/2²-1,3²+1/3²-1,.,（n+1）²+1/（n-1）²-1的前n项和Sn

求数列2²+1/2²-1,3²+1/3²-1,.,（n+1）²+1/（n-1）²-1的前n项和Sn
如确认An＝(n+1)²+{1/[(n+1)²-1]},可按下述方法求
Sn=[2²+3²+……+(n+1)²]+{1/(2²-1)+1/(3²-1)+……+1/[(n+1)²-1]}
={-1²+(n+1)(n+2)(2n+2)/6}+{1/(1*3)+1/(2*4)+1/(3*5)+……+1/[(n)(n+2)]}
=-1+[(n+1)²(n+2)/3]+{1+(1/2)-[1/(n-1)]-[1/(n+1)]}/2
=(-1/4)+[(n+1)²(n+2)/3]-[n/(n²-1)]