数列an的前n项和为Sn,且Sn^2-2Sn-anSn+1＝0,n＝1,2,3,……求表达Sn式

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Sn^2-2Sn-anSn+1=0
S1^2-2S1-a1S1+1=0
-2S1+1=0
S1=a1=1/2
an=Sn-S(n-1)
Sn^2-2Sn-[Sn-S(n-1)]Sn+1=0
2Sn-S(n-1)Sn=1
2-S(n-1)=1/Sn
1-S(n-1)=1/Sn -1=(1-Sn)/Sn
1/[1-S(n-1)]=Sn/(1-Sn)=-1+1/(1-Sn)
1/(1-Sn)-1/[1-S(n-1)]=1
1/(1-Sn)=1/(1-S1)+(n-1)*1
=1/(1-1/2)+n-1
=n+1
1/(1-Sn)=n+1
1-Sn=1/(n+1)
Sn=1-1/(n+1)=n/(n+1)
Sn=n/(n+1)

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