已知a1=1,an大于0,sn=1/4*(an+1)^2求通项公式
问题描述：
已知a1=1,an大于0,sn=1/4*(an+1)^2求通项公式
答
Sn=(an+1)^2/4=(an^2+2an+1)/4Sn-1=[a(n-1)+1]^2=[(a(n-1)^2+2a(n-1)+1]/4Sn-Sn-1=an=[an^2+2an-a(n-1)^2-2a(n-1)]/44an=an^2+2an-a(n-1)^2-2a(n-1)an^2-2an=a(n-1)^2+2a(n-1)(an-1)^2=[a(n-1)+1]^2又a1=1,an>0an-1=...