Divergence test for $\sum_{n=1}^{\infty}\ln (1+\frac{1}{n})^n$. I am trying to prove that this is divergent 
$$\sum_{n=1}^{\infty} \left(1+\dfrac{1}{n}\right)^n$$
by finding the limit of 
$$\ln \left(1+\dfrac{1}{n}\right)^n$$
I know its $e$ and I am trying to arrive at that value by this
$$\ln y = n \ln(1 + \dfrac{1}{n})\\= \dfrac{\ln(1 + \dfrac{1}{n})}{\dfrac{1}{n}}$$
and I am already lost at this indeterminate form.

But if you want to prove that diverges is not most easy: 
$$\sum (1+1/n)\leq \sum (1+1/n)^n?$$
