Q$6($a$)$ Find a formula for the $n$th term of the sequence and test the convergence.

$\frac{1}{81},-\frac{1}{27},\frac{1}{9},-\frac{1}{3},1$dots

$($b$)$ Use the Limit Comparison Test to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n}{(4n+1{)}^{\frac{3}{2}}}$ converges or diverges.

$($c$)$ Use the Ratio Test to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^2}{n!3^n}$ converges absolutely or diverges.