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.

This is the indeterminate form $1^\infty$.
So set $L = \lim_{n \rightarrow \infty} (1+\frac{1}{n})^n$
Then
$$\ln(L) = \lim_{n \rightarrow \infty} n \ln{(1+\frac{1}{n})} = \lim_{n \rightarrow \infty} \frac{\ln(1 + 1/n)}{1/n}$$
Apply L'Hopital's and then work backwards, solving for $L$.
