Power series function - convergence interval

Question

Could someone help me finding the function and convergence interval for following power series? I don't need a step by step answer, but I'm not entirely sure where to start.

$\sum_{n=0}^{+\infty} (\frac{-1}{2})^n\cdot \frac{x^{3n+3}}{3n+3}$

Thanks in advance!

Answer 1

Here is an answer for where to start:

If you are unfamiliar with power series inversion, have a textbook or other table of these things handy.

You should notice that the series for $\textrm{log}(1+x)$ near zero has two similarities with your series.

1) It is alternating

2) And has terms of the form $\frac{x^k}{k}$.

I'll let you take it from there. You should be able to invert this series by substitution.