Use an appropriate test to determine whether the following series converges.

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{k}{e^{7k}}$

Select the correct choice below and fill in the answer box to complete your choice.

$($Type an exact answer.$)$

A$.$ The series diverges by the Integral Test. The value of the integral ${\displaystyle \underset{1}{\overset{}{}}}\frac{x}{e^{7x}}dx$ is

B$.$ The series divers $$ by the Divergence Test. The value of $\underset{k}{lim}\frac{k}{e^{7k}}$ is

C$.$ The series converges by the Divergence Test. The value of $\underset{k}{lim}\frac{k}{e^{7k}}$ is

D$.$ The series diverges. It is a $p-$series with $p=$

E$.$ The series converges by the Integral Test. The value of the integral ${\displaystyle \underset{1}{\overset{}{}}}\frac{x}{e^{7x}}dx$ is

F$.$ The series converges. It is a $p-$series with $p=$