For which power do these series converge for odd and even termes

Question

Hi I really don’t know how to solve this question:

For which a do these series converge ?
$(\sum_{i=0}^n \frac{1}{i!})^a $ only if i is odd
$\sum_{i=0}^n \frac{(2^i)}{i!}$ only if i is even

I know the even serie converge to something smaller than e^2 But for the odd one I don’t know how to handle it.

Any idea ? Thanks