在数列{An}中,已知A1=1,An=2Sn^2/(2Sn-1),(n>=2)求An

问题描述:

在数列{An}中,已知A1=1,An=2Sn^2/(2Sn-1),(n>=2)求An

An=2Sn^2/(2Sn-1),Sn=S(n-1)+An代入上式得 An=2(S(n-1)+An)^2/(2S(n-1)+An)-1),2(S(n-1))^2+An(2S(n-1)+1)=0,An=-2(S(n-1))^2/(2S(n-1)+1),又An=2Sn^2/(2Sn-1),故 -(S(n-1))^2/(2S(n-1)+1)=Sn^2/(2Sn-1),(Sn-S(n-1))...