$(14$ points$)$ Consider the following series

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{sin5n}{n^5}$

Answer the following questions:

$q,1.(1$ point$)$ Is this a geometric series?

Not a Pomilor one, but can be

$q,2.(1$ point$)$ Is this a $p$ series?

yes

$+$

$-2$

$3.(2$ point$)$ Can you tell whether this series is convergent by the n$-$th term test? Why?

convergent

$q,4.(1$ point$)$ Is this an alternating series?

yes

$5.(1$ point$)$ Is this a positive series?

$6.(4$ point$)$ Does this series converge absolutely$?$ Why?

${\displaystyle \underset{n=1}{\overset{}{}}}|\frac{sin5n}{n^5}{|}_k\frac{1}{n^2}=($