$(6)$ Use a convergence test to classify each of the following series as convergent or divergent. You need only submit any $5$ of the problems for credit. We recommend that you do the remainder for practice.

a$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{3}{n{2}^n}$

b$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{si{n}^{2}n}{n\sqrt[\phantom{2}]{n}}$

c$){\displaystyle \underset{n=2}{\overset{}{}}}sin(\frac{1}{n})$

d$){\displaystyle \underset{n=2}{\overset{}{}}}\frac{1}{n^2-1}$

e$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^n}{n!}$

f$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{lnn}{n^2}$

g$){\displaystyle \underset{n=3}{\overset{}{}}}\frac{l{n}^{5}n}{n}$

h$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{arctann}{n}$