数列an中,a1=3 am+n=am.an 则sn/an的极限是多少

题目

数列an中,a1=3 am+n=am.an 则sn/an的极限是多少

答案

a(m+n)=am.an
m=1
a(n+1)=a1.an
=3an
{an}是等比数列,q=3
an = 3^(n-1) .a1
= 3^n
Sn = (3/2)(3^n-1)
lim(n->∞)Sn/an
=lim(n->∞) (3/2)( 1- 1/3^n)
=3/2