Why does $\left(1+ 1/k\right)^k$ converge to $e$ as $k \to\infty$? I came across this when learning about sequences and series. No one proved it to me tho! Is there a link anywhere? Or would it be beyond what I know? (First term of analysis)

Usually Sometimes, $e$ is defined to be $\lim_{n \to \infty}\left(1+\frac 1n\right)^n$. What might need to be proved is that that limit exists.
Incidentally, this can be proved as well
$$\lim_{n \to \infty}\left(1+\frac 1n\right)^n = \sum_{n = 0}^\infty \frac{1}{n!}$$
I think a discussion of these things can be found in Rudin's PMA.
