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

Consider the product
$$
\left(1+x\right)^2\left(1-2x\right)=1-3x^2-2x^3
$$
which leads to 
$$
\left(1+\frac1n\right)^{2n}\left(1-\frac2n\right)^n
=\left(1-\frac3{n^2}-\frac2{n^3}\right)^n
$$
By Bernoulli, one gets for the right side
$$
1\ge\left(1-\frac3{n^2}-\frac2{n^3}\right)^n\ge1-\frac3{n}-\frac2{n^2}
$$
so by squeeze theorem its limit is $1$. By the quotient rule of limits, 
$$
\lim_{n\to\infty}\left(1-\frac2n\right)^n=\left(\lim_{n\to\infty}\left(1+\frac1n\right)^{n}\right)^{-2}
$$
