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)

It's like calculating limit of function $\lim_{x\to \infty}(1+\frac1x)^x$
This is of the the form $1^{\infty}$.
So $$\lim_{x\to \infty}\left(1+\frac1x\right)^x = e^{\lim_{x\to\infty}((1+\frac1x)-1)(x)}$$
$$= e^1$$
$$= e$$
