Use the direct comparison test $to$ determine whether

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n}{\sqrt[\phantom{2}]{2n^4-1}}$ converges $or$ diverges.

Select one:

$a.$ Converges $by$ comparison with ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{2}}\frac{1}{n^2}$

$b.$ Converges $by$ comparison with ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{2}}\frac{1}{n^3}$

$c.$ Diverges $by$ comparison with ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{2}}\frac{1}{\sqrt[\phantom{2}]{n}}$

$d.$ Diverges $by$ comparison with ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{2}}\frac{1}{n}$