a1=1,Sn=n²×an,求an通项公式

a1=1,Sn=n²×an,求an通项公式
a1=1,Sn=n²×an,求an通项公式

a1=1,Sn=n²×an,求an通项公式
An = Sn - Sn-1 = n²×An - (n-1)²×An-1
===> (n²-1)An = (n-1)²An-1
===> (n+1)An = (n-1)An-1
===> An = (n-1)/(n+1) An-1
===> An = (n-1)/(n+1)×(n-2)/n ×(n-3)/(n-1)×……× 3/5 × 2/4 × 1/3
===> An = 2/[n(n+1)]