{an}{bn}等差,前n项和的比为Sn/Tn=(2n+1)/(3n-2),求lim an/bn
问题描述:
{an}{bn}等差,前n项和的比为Sn/Tn=(2n+1)/(3n-2),求lim an/bn
答
Sn/Tn=(2n+1)/(3n-2),又:an/bn=S(2n-1)/T(2n-1)=[2(2n-1)+1]/[3(2n-1)-2]
=[4n-1]/[6n-5]
则:lim an/bn=2/3