Determine whether the following series converge.

(a) $\displaystyle \sum_{k=1}^{\infty} 2ke^{-k^{2}}$ ? Converges Diverges

(b) $\displaystyle \sum_{k=1}^{\infty} \left(1+\frac{2}{k}\right)^{-k}$ ? Converges Diverges

(c) $\displaystyle \sum_{k=1}^{\infty} \frac{1}{\sqrt{k^{2}+5}}$ ? Converges Diverges