$(4$ pts$)6)$ Briefly explain what is wrong with the following attempt to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^2+2}$ converges or diverges.

Use Comparison Test with $b_n=\frac{1}{1}=1$

$($taking out the $n^2+2$ from the bottom$)$

Since $\underset{n}{lim}1=10,{\displaystyle \underset{n=1}{\overset{}{}}}1$ diverges by nth term test.

Therefore, ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^2+2}$ also diverges by Comparison Test.