$\displaystyle \sum_{n=1}^{\infty}{\frac{(n+1)^{2n}}{2^nn^{2n}}}$

$\displaystyle \sum_{n=2}^{\infty}{({{{\frac{n}{n+1}}})^{n^{2}}}}$

I have tried both tests on the series, and both yield the limit going to 1 (test fails, may diverge or converge).

Is there a way to show either diverge or converge by another test, or comparison theorem? Can't seem to find anything! Will keep trying though!

Thank you!!