已知数列{an}中an不等于0(n>=1),a1=0.5,前n项和Sn满足:an=2(Sn)^2/(2Sn-1)(n>=

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已知数列{an}中an不等于0(n>=1),a1=0.5,前n项和Sn满足:an=2(Sn)^2/(2Sn-1)(n>=2),求数列{an}的通项公式.

$已知数列{an}中an不等于0(n>=1),a1=0.5,前n项和Sn满足:an=2(Sn)^2/(2Sn-1)(n>=$

2(Sn)^2/(2Sn-1)=Sn-S(n-1)得1/Sn-1/S(n-1)=2即{1/Sn}为等差n>1,d=2,1/S2=4
a2=S2-a1=2(S2)^2/2S2-1
S2=1/4
1/Sn=2n
an=1/2n(1-n)

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