Consider the series

${\displaystyle \underset{n=1}{\overset{}{}}}$ I ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^{\frac{n}{2}}}$

Write an inequality comparing $\frac{1}{\sqrt[\phantom{2}]{n^{3}4n-1}}$ to $\frac{1}{n^{\frac{9}{7}}}$ for $n1.$

$($Txpress numbers in exact form. Use symbolic notation and fractions where needed.$)$

iney $$

Draw a conclusion about ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{n^{3}4n-1}}.$

The series converges by the Direct Comparison Tea since ${\displaystyle \underset{x=1}{\overset{}{}}}\frac{1}{n}$ converges.

The neries diverges by the Direct Comparison Teat since ${\displaystyle \underset{m=1}{\overset{}{}}}\frac{1}{n}$ diverges.

It is not possible to draw a conclusion based on this information.