I'm familiar with binomial expansions in the form of $\displaystyle (a+b)^n$, where n is an integer. However, today I came across the following:

$\displaystyle \sqrt[3]{1+\frac{1}{n^3}} \:=\: 1+\frac{1}{3n^3}+\frac{1}{9n^6}+\frac{5}{81n^9} + \ldots$

How is that result reached? Is there a general expression for the expansion of $\displaystyle (a+b)^n$ where n is not an integer?

(I searched online, but I didn't find anything that explained what I was after.)