QUESTION $4$

Using direct comparison test, the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5+2n}{(n^2+1{)}^2}$ is

A$.$ convergent because $\frac{5+2n}{(n^2+1{)}^2}\frac{3}{n^4}$ for all $n1$

B$.$ convergent because $\frac{5+2n}{(n^2+1{)}^2}\frac{7}{n^3}$ for all $n1$

c$.$ divergent because $\frac{5+2n}{(n^2+1{)}^2}\frac{5}{n^2}$ for all $n1$

D$.$ divergent because $\frac{5+2n}{(n^2+1{)}^2}\frac{5}{n}$ for alll $n1$

E$.$ divergent because $\frac{5+2n}{(n^2+1{)}^2}\frac{2}{n^{\frac{1}{4}}}$ for all $n1$