设等差数列{an},{bn}的前n项和分别为An,Bn,切An/Bn=(3n+1)/(2n-5),求liman/bn
问题描述：
设等差数列{an},{bn}的前n项和分别为An,Bn,切An/Bn=(3n+1)/(2n-5),求liman/bn
答
an=a1+(n-1)d,bn=b1+(n-1)e,d、e是公差
An/Bn=[2a1+(n-1)d]/[2b1+(n-1)e]=[dn+(2a1-d)]/[en+(2b1-e)]=(3n+1)/(2n-5)
对比系数知d/e=3/2
所以lim an/bn=lim [a1+(n-1)d]/[b1+(n-1)e]=d/e=3/2