We define the following relation:
$$y = \frac{(1+x)^n - 1}{x}$$
Alternatively,
$$y = \sum_{k = 1}^n {n \choose k} x^{k-1}$$
Where $n$ is an integer and $x$ and $y$ are positive real numbers. How can we find a closed form expression for $x$ in terms of $y$ and $n$?