test for convergence/divergence help!

kyrax

1. The problem statement, all variables and given/known data

test if (1+4^n)/(1+3^n) is convergent or divergent.


2. Relevant equations



3. The attempt at a solution

using the ratio test. i got it equal to 5/4 which is > 1, so it diverges. can someone check this? what other methods are available?

LCKurtz

What you have given is a sequence, not a series and the ratio test applies to series convergence. Did you mean to test

[tex]\sum_{n=1}^{\infty}\frac{1+4^n}{1+3^n}[/tex]

for convergence? If so the ratio test is appropriate, but I don't get 5/4 for its limit.