$\displaystyle (1+\frac{1}{n})^n\ge2, \forall n \in \mathbb{Z} : n>0$

So the easiest way I think is to use binomial theorem.

I've gotten to:

$\displaystyle \Sigma_{k=0}^{n-1}(_k^n)1^k(\frac{1}{n})^{n-k}+1$

So I guess I essentially have to prove:

$\displaystyle \Sigma_{k=0}^{n-1}(_k^n)1^k(\frac{1}{n})^{n-k}>1$