I'm asked to prove the question above.
I need to show that if $(a_n)$ is an increasing sequence of integers then: $\lim_{n\to\infty}\left(1+\frac{1}{a_n}\right)^{a_n}=e$
I was thinking of showing that $\lim_{n\to\infty}(a_n)=\infty$ and then, by definition, I can say that there exists a natural number $N$, such that for every $n>N, a_n>0$ and so $(a_n)^\infty_{n=N}$ is a sub-sequence of $(1+\frac{1}{n})^n$ and therefore shares the same limit- $e$
Any ideas?