I would like to know where I could apply the expression as part of other equation
$$\bigg( 1 + \frac{x}{r} \bigg)^r$$
considering $r \in Z$. It means, in what kind of problem I can use this expression.
For me, it does not matter the number $r$. For example, when $r \to \infty$ it becomes $exp(x)$ which can be used in lots of engineering problems