Write an inequlity comparing $\frac{n^2-2}{n^5+2}$ with $\frac{1}{n^3}$ for $n1.$

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

inequalit

Use this inequality to draw a conclusion about the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^2-2}{n^5+2}.$

The series diverges by the Direct Comparison Test because ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^3}$ also diverges.

The series converges by the Direct Comparison Test because ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^3}$ also converges.

It is not possible to draw a conclusion about the convergence of the series because ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^3}$ diverges.