Converting Function to Power Series

What:

Sometime’s you may get a function in the form $f(x)=\frac{1}{1+x^3}$ and want it in a Power Series representation.

How to convert Function to Power Series:

Remember, by definition of the sum of an infinite sequence, a series: ${\sum }_{n=0}^{\infty }a{r}^n=a+ar+a{r}^{2+\dots }=\frac{a}{1-r}$
when $|r|<1$. Use this fact to manipulate a function into the RHS of above. You can then extract $a$ and $r$ and put them in the form of the LHS.

From here, you can pretty easily find the Radius of Convergence.