$\displaystyle \sum_{n=1} ^\infty (\sqrt[3]{n})^{3n} * {(\Pi-2)}^{-4n^2}

$

Does this converge or diverge and how?

$\displaystyle \sum_{n=1} ^\infty {sinh(1/e^x)}$

I'm leaning on converge for this one because

the limit of $\displaystyle (1/e^x)$ = 0

so,

$\displaystyle \sum_{n=1} ^\infty {sinh(1/e^x)}$

Converges by the Limit Comparison Test?