等差数列列｛an｝的前n项和为Sn,公差为2,则lim(n→∞)Sn/an^2=?_数学解答

等差数列列｛an｝的前n项和为Sn,公差为2,则lim(n→∞)Sn/an^2=?

人气：154 ℃　时间：2019-10-23 04:21:19

解答

a(n)=a+(n-1)d,[a(n)]^2=[a+(n-1)d]^2=[nd+a-d]^2,s(n)=na+n(n-1)d/2=(d/2)n^2+n(a-d/2),s(n)/[a(n)]^2=[(d/2)n^2+n(a-d/2)]/[nd+a-d]^2=[d/2+(a-d/2)/n]/[d+(a-d)/n]^2,lim(n->无穷大){s(n)/[a(n)]^2}=lim(n->无穷...