Show that $\frac{n}{1+n}<\ln{\left(1+\frac{1}{n}\right)^n}<1$ for $n=1,2,3,\dots$

Question

I am struggling to see how to use the following two pieces of information (which I have proven):

$\frac{1}{n}< \ln{n}$ for $n=2,3,4,\dots$

and

$\ln{(1+n)}<n$ for $n=1,2,3,\dots$

to show that

$\frac{n}{1+n}<\ln{\left(1+\frac{1}{n}\right)^n}<1$ for $n=1,2,3,\dots$

I know it's more than likely something very straight forward.