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

Let $y = \left(1+ -\frac2n\right)^n$

$$\log y = n\log\left(1+ -\frac2n\right)$$
$$\log y = {(-2/n)n\log\left(1+ -\frac2n\right)\over (-2/n)}$$
$$ y = \exp\left({-2\log\left(1+ -\frac2n\right)\over (-2/n)}\right)$$
$$ \lim_{n\to\infty} y =
\lim_{n\to\infty} \exp\left({-2\log\left(1+ -\frac2n\right)\over (-2/n)}\right)= \exp\left(\lim_{n\to\infty}{-2\log\left(1+ -\frac2n\right)\over (-2/n)}\right)=\exp(-2)= e^{-2}$$
