Question

数列{an}中,a1=1,当n>1时,2Sn^2=2anSn-an,求通项an

Answer 1

当n>1时,an=sn-sn-1代入化简得：

1/Sn-1/Sn-1=2

所以：1/Sn=2n-1

所以：Sn=1/(2n-1)

当n>1时,an=sn-sn-1

=-2/[(2n-1)(2n-3)]

当n=1时a1=1也符合

an=-2/[(2n-1)(2n-3)]