$(4$ pts$)11)$ Briefly explain what is wrong with the following attempt to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{cosn}{n}$ converges or diverges.

Use $n$th term test by checking $\underset{n}{lim}{a}_n=\underset{n}{lim}\frac{cosn}{n}$ As $n$ goes to $,cosn$ will oscillate between $-1$ and $1$ however $n$ will get larger and larger. So $\underset{n}{lim}\frac{cosn}{n}=0$ which means ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{cosn}{n}$ converges.