Use binomial expansion to find the Maclaurin series of the function,

$\displaystyle f(x) = \left( \frac{x^{2}}{1+x^{3}} \right)^{3}$

What is the open interval of convergence? Express your answer in sigma notation and simplify as much as possible.

See figure attached for my attempt at the solution.

If someone could verify my solution that'd be great!