等差数列{an},{bn}的前n项和分别为An,Bn,切An/Bn=2n/3n+1,求lim(n→∞)an/bn

An=[2n/(3n+1)]Bn
An-1=[2n/(3n+1)]Bn-1
lim(n→∞)an/bn=lim(n→∞)[An-An-1]/[Bn-Bn-1]
=lim(n→∞)[2n/(3n+1)][Bn-Bn-1]/[Bn-Bn-1]
=lim(n→∞)[2n/(3n+1)]=2/3