Expanding $(1+x^3)^{-1/3}$

Question

I have tried to create a sum formula $$ \sum_{n=0}^\infty \begin{pmatrix} -1/3 \\ n \\ \end{pmatrix}x^{3n} $$

However, the first term I found $\frac{-x^3}3$ was not true. I think I have to substitute $x^3$ with something but I don't know how.

Answer 1

For this particular expansion try using the well know form:

$$\left(1+x\right)^n =1+ \frac{n}{1!}x^1+\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+\cdots $$