Euler's Limit -- Revisited

Abstract

The aim of this short note is that if $\{a_n\}$ and $\{b_n\}$ are two sequences of positive real numbers such that $a_n\to +\infty$ and $b_n$ satisfying the asymptotic formula $b_n\sim k\cdot a_n$, where $k>0$, then $\underset{n\to \infty }{\lim }{\left(1+\frac{1}{a_n}\right)}^{b_n}=e^k$.

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