Help me please with these 2 questions:

1.Does it converge or diverge? :
$$ \sum\_{n=2}^{\infty }2^{n}\left ( \frac{n}{n+1} \right )^{n^{2}} $$

2.Check out absolute and conditional convergence of: $x>0 $

$$ \sum\_{n=1}^{\infty }\sin (n)\sin \frac{x}{n} $$

Thanks a lot!