Homework$-9$: Problem $6$

$(5$ points$)$

Match each of the following with the correct statement.

A$.$ The series is absolutely convergent.

C$.$ The series converges, but is not absolutely convergent.

D$.$ The series diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-3{)}^n}{n^3}$

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}\frac{(6+n)2^n}{(n^2)3^{2n}}$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^{n+1}}{5n+7}$

$q,4.{\displaystyle \underset{n=1}{\overset{}{}}}\frac{sin(4n)}{n^3}$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(n+5)!}{n!3^n}$