问道数列的题目.
问题描述：
问道数列的题目.
数列{An},An＝2(Sn^2)/(2Sn－(1))(n＞＝2),S1＝1,求An.
答
An＝2(Sn^2)/(2Sn－1)2An*Sn-An=2Sn^22Sn^2-2S(n-1)*Sn-Sn+S(n-1)=2Sn^21/Sn-1/S(n-1)=21/S1=11/Sn=2n-1Sn=1/(2n-1)An=Sn-S(n-1)=1/(2n-1)-1/(2n-3)=-2/(2n-1)(2n-3)(n>=2)