1. Is the series Sigma $\displaystyle (-1)^n * (n!)^2/((2n)!)$ convergent

2. Determine the radius of convergence of the power series Sigma

$\displaystyle (-1)^n * ((n+3)/(3^n+4^n)) * x^(3n)$

3. Is the series Sigma$\displaystyle n!/(n^n)$convergent

Thx guys!