Question

数列an的前n项和为Sn,且Sn^2-2Sn-anSn+1＝0…在线等高手!

Answer 1

字数受限简单叙述

Sn^2-2Sn-anSn+1=0

S1^2-2S1-a1S1+1=0

S1=a1=1/2

an=Sn-S(n-1)

Sn^2-2Sn-[Sn-S(n-1)]Sn+1=0

1/(1-Sn)=1/(1-S1)+(n-1)*1

=n+1

1/(1-Sn)=n+1

Sn=1-1/(n+1)=n/(n+1)

Sn=n/(n+1)