## Find out where this power series converges

1. The problem statement, all variables and given/known data
Find out where this power series converges.

Ʃ(xn2n) / (3n + n3)

2. Relevant equations

3. The attempt at a solution

I'm trying to use the ratio test to solve it. I end up with the following equation, which I am unable to reduce further:

pn = 2x (3n + n3)/[(3)(3)n+n3(1+1/n)3]

 PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire
 My guess is, since $3^n$ goes to infinity faster than $n^3$ (exponentials are faster than polynomials), is that your ratios go to $\frac{2}{3}x$. Tnen you want $|x|<\frac{3}{2}$. Not sure what happens at the boundaries. To check the limit I guessed at, maybe use l'Hopital's rule 3 times?