Use any method to determine whether the series converges.

(a) $\displaystyle \sum_{k=1}^{\infty} \frac{\left(k+3\right)!}{e^{k^{2}}}$

? Converges Diverges

(b) $\displaystyle \sum_{k=1}^{\infty} \frac{3^{k}+k}{k!+5}$

? Converges Diverges