Test for convergence/divergence help

[kyrax]

Homework Statement

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

Homework Equations

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

$$\sum_{n=1}^{\infty}\frac{1+4^n}{1+3^n}$$

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