Binomial expansion for $n^{\rm th}$ root

Question

The binomial expansion of the square root of $1+n$ is well known:

$$ (1+n)^{1/2}=\sum_{i=0}^{\infty}\binom{1/2}{i}n^i=1+\frac{n}{2}-\frac{n^2}{8}+o(n^3). $$

But what do we know about the expansion of $(1+n)^{1/m}$ for positive integer $m>2$?