Use the Comparison Test or the Limit Comparison Test to determine whether the following series converges.

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{4si{n}^{4}k}{k^3}$

Choose the correct answer.

A$.$ The Comparison Test with ${\displaystyle \underset{?}{\overset{?}{}}}\frac{4}{k^3}$ shows that the series converges.

B$.$ The Comparison Test with ${\displaystyle \underset{?}{\overset{?}{}}}\frac{4}{k^3}$ shows that the series diverges.

C$.$ The Limit Comparison Test with ${\displaystyle \underset{?}{\overset{?}{}}}\frac{4}{k^3}$ shows that the series converges.

D$.$ The Limit Comparison Test with ${\displaystyle \underset{?}{\overset{?}{}}}\frac{4}{k^3}$ shows that the series diverges.