This is probably an easy one, but I'm having trouble solving this series:
$$\sum_{n=1}^{\infty}\frac{x^2}{(n+1)\sqrt[3]{n+2}}$$
I've tried to use the ratio test, but the result is 1, so the test is inconclusive. I've also tried Raabe-Duhamel's test, but (if I did it right) my result was $\infty$.
Assuming that $x=1$*, the general term is asymptotic to $n^{-4/3}$ so that the series converges.
*In case the exponent of $x^2$ would be incorrect.