帮帮忙，数列中,A1=1,An=(2sn^2)/(2Sn-1)(n=>2),求这个的前n项和

an=2Sn^2/(2Sn-1)

2an*Sn-an=2Sn^2,因为an=Sn-S(n-1)

so,2[Sn-S(n-1)]*Sn-Sn+S(n-1)=2Sn^2
so,S(n-1)-Sn=2S(n-1)*Sn
so,[1/Sn]-[1/S(n-1)]=2
so,[1/S(n-1)]-[1/S(n-2)]=2
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so,[1/S2]-[1/S1]=2
全部相加，得到：[1/Sn]-[1/S1]=2（n-1)
S1=a1=1

so,1/Sn=2n-1

Sn=1/(2n-1),带入an=2Sn^2/(2Sn-1) ，得到：an=(-2)/[(2n-3)*(2n-1)]