$\underset{n}{lim}\sqrt[n]{a_n}=$

a$)$ Show that the series converges if

b$)$ Let

$a_n=\{\begin{array}{ccc}\frac{n}{2^n}& ifnis\text{o}\text{d}\text{d}& \\ \frac{1}{2^n}& ifnis\text{e}\text{v}\text{e}\text{n}& \end{array}$

Does ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ converge?