等比数列{an},首项a1>0,公比q>0,Sn为前n项和,记Gn=a1^2+a^2+…+an^2.求lim(n趋近于正无穷)(Gn/Sn)
问题描述：
等比数列{an},首项a1>0,公比q>0,Sn为前n项和,记Gn=a1^2+a^2+…+an^2.求lim(n趋近于正无穷)(Gn/Sn)
答
Gn=a1^2+a^2+…+an^2=a1^2q^0+a1^2q^2+…+a1^2q^(2n-2)=a1^2(q^2n-1)/(q^2-1)Sn=a1(q^n-1)/(q-1)limGn/Sn=lim{[a1^2(q^2n-1)/(q^2-1)]/[a1(q^n-1)/(q-1)]}=lim[a1(q^n+1)/(q+1)]当q1,无极限