已知数列{An}与{Bn}都是公差不为零的等差数列,且limAn/Bn=2,求lim(A1+A2+……+An)/(n*B2n)的值!

问题描述:

已知数列{An}与{Bn}都是公差不为零的等差数列,且limAn/Bn=2,求lim(A1+A2+……+An)/(n*B2n)的值!

设{An}的公差为d1,{Bn}的公差为d2 因为limAn/Bn=lim[a1+(n-1)d1]/[b1+(n-1)d2] =lim[a1/n+(1-1/n)d1]/[b1/n+(1-1/n)d2] =(0+d1)/(0+d2) =d1/d2 =2A1+A2+……+An=2A1+n(n-1)d1/2nB2n=n(b1+(2n-1)d2)所以lim(A1+A2+…...