$(4$ pts$)2)$ Briefly explain what is wrong with the following attempt to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{3n^2}{2n^2+n}$ converges or diverges.

Check $\underset{n}{lim}{a}_n$

$=\underset{n}{lim}\frac{3n^2}{2n^2+n}$

$=\underset{n}{lim}\frac{3n^2}{2n^2+n}*\frac{\frac{1}{n^2}}{\frac{1}{n^2}}$

$=\underset{n}{lim}\frac{3}{2+\frac{1}{n}}$

$=\frac{3}{2}$

So ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{3n^2}{2n^2+n}$ converges to $\frac{3}{2}$