在数列｛an｝中,已知a1=1,当n≥2时,an,Sn,Sn-1/2成等比数列,求｛an｝的通项公式

an,Sn,Sn-1/2成等比数列an(Sn-1/2)=Sn^2a2(S2-1/2)=S2^2a2(a2+1/2)=(a2+1)^2a2=-2/3a3(S3-1/2)=S3^2a3(a3-1/6)=(a3+1/3)^2a3=-2/33[Sn-S(n-1)](Sn-1/2)=Sn^2-(1/2)Sn-S(n-1)Sn+(1/2)S(n-1)=0-(1/2)Sn+(1/2)S(n-1)=S(n-1)Sn1/Sn-1/S(n-1)=-21/Sn=(1/S2)+(-2)(n-2)=[1/(1-2/3)]+(-2)(n-2)=3+(-2)(n-2)=-2n+7Sn=1/(-2n+7)S(n-1)=1/(-2n+5)an=Sn-S(n-1)=1/(-2n+7)-1/(-2n+5)an=1/(-2n+7)-1/(-2n+5);