Sequence Interval of convergence

Question

I could someone help me with the following sequence of functions of which I attempted to find the interval of convergence, but I couldn't get it to match with the solution I get from WolframAlpha (which doesn't support a step-by-step solution) unfortunately.

Thanks a lot in advance!

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

Answer 1

try rewriting as $$ S = x^2 \sum_{n=0}^{+\infty} (\frac{-x^3}{2})^n $$