Infinite series : testing for convergence, exponential involved.

I am asked to see if the summation of (3^n+n)/(4^n-3^n) converge or not.

I have tried ratio test, comparison test and limit comparison test, but none of them work (at least for me provided my limited skills in math)

By comparison test I used 3^n/4^n and 1/(4^n-3^n) for comparison, the same goes for limit comparison (I break the summation up into two part, one with 3^n on top and the other with n on top)

How should I attack the problem? Thank you!