$($a$)(3$ points$)$ Show that if a series ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ converges absolutely$,$ then the series ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n^2$ converges.

$($b$)(3$ points$)$ If a series ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ converges, is it true that the series ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n^2$ must converge? Justify your answer.

$($c$)(3$ points$)$ If $a_{n}0$ and the series ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ converges, then show by examples that the series ${\displaystyle \underset{n=1}{\overset{}{}}}\sqrt[\phantom{2}]{a_n}$ may converge or may diverge.