已知数列an满足an>0,Sn=[(an+1)/2]^2,bn=(-1)^n*Sn,求b1+b2+……+bn
问题描述：
已知数列an满足an>0,Sn=[(an+1)/2]^2,bn=(-1)^n*Sn,求b1+b2+……+bn
答
4Sn=(an+1)^24S(n-1)=[a(n-1)+1]^2an=Sn-S(n-1)所以相减4an=(an+1)^2-[a(n-1)+1]^2(an+1)^2-4an=[a(n-1)+1]^2(an-1)^2=[a(n-1)+1]^2an-1=a(n-1)+1或an-1=-a(n-1)-1an=a(n-1)+2或an=-a(n-1)an>0所以an=-a(n-1)不成立...