当n>=2时
Sn=n(2n-1)an
S(n-1)=(n-1)(2n-3)a(n-1)
an=Sn-S(n-1)=n(2n-1)an-(n-1)(2n-3)a(n-1)
an/a(n-1)=(2n-3)/(2n+1)
所以
an=an/a(n-1) * a(n-1)/a(n-2) * a(n-2)/a(n-3) * ...* a2 / a1 * a1
=(2n-3)/(2n+1) * (2n-5)/(2n-1) * (2n-7)/(2n-3) * ...* 1/5 * 1/3
=1/((2n+1)(2n-1))
=1/(4n^2-1)
当n=1时也成立
所以an=1/(4n^2-1)