Find the limit of $(1-\frac2n)^n$ I am trying to find the limit of $$(1-\frac2n)^n$$
I know how $e$ is defined and I am sure the prove will involve substituting a term with $e$ at some point. But I do not really know where to start. I tried rewriting the term, simplifying it, using the binomial theorem, but all that does not seem to work out that well. Where do I start?
Edit: As $n$ goes towards infinity

Note that
$$
\left(1-\frac2n\right)^n = \left(1-\frac{1}{n/2}\right)^n = \left(\left(1-\frac{1}{n/2}\right)^{n/2}\right)^2
$$
Now take the limit as $\frac n2 \to \infty$.
