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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

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  • $\begingroup$ It is not clear to me what you are asking. Clearly small values or $r$ give different results: e.g. $1+x \not=e^x$ for non-zero $x$ $\endgroup$
    – Henry
    Commented May 17, 2023 at 16:51
  • $\begingroup$ In which math, physical or engineering models I can find such expression? $\endgroup$
    – K Z Nobrega
    Commented May 17, 2023 at 18:10
  • $\begingroup$ See compound interest formula $\endgroup$
    – Тyma Gaidash
    Commented May 17, 2023 at 19:19

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