Sn=n^2An - n(n-1)Sn-1=(n-1)^2An-1 - (n-1)(n-2)n>=2,An=Sn-sn-1=[n^2An - n(n-1)]-[(n-1)^2An-1 - (n-1)(n-2)] An=n^2An-(n-1)^2An-1-2n+2An=(n-1)/(n+1)An-1 +2/(n+1)A2=1,A3=1.....可以证明 An=1所以 Sn=Sn-1 +1 (n>=2)Sn=n