Determine whether the Ratio Test is inconclusive $($that is$,$ it fails to give a definite answer$),$ conclusive $($convergent$),$ or conclusive $($divergent$)$ for each series.

$($a$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{3}{n^3}$

inconclusive

conclusive $($convergent$)$

conclusive $($divergent$)$

$($b$){\displaystyle \underset{n=3}{\overset{}{}}}\frac{n}{5^n}$

inconclusive

conclusive $($convergent$)$

conclusive $($divergent$)$

$($c$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-4{)}^{n-1}}{\sqrt[\phantom{2}]{n}}$

inconclusive

conclusive $($convergent$)$

conclusive $($divergent$)$

$($d$){\displaystyle \underset{n=3}{\overset{}{}}}\frac{\sqrt[\phantom{2}]{n}}{1+n^2}$

inconclusive

conclusive $($convergent$)$

conclusive $($divergent$)$