Determine whether the series ${\displaystyle \underset{m=2}{\overset{}{}}}\frac{7}{4^m}$ converges or diverges. If it converges, find its sum.

Select the correct choice below and, if necessary, fill in the answer box within your choice.

A$.$ The series converges because $\underset{n}{lim}\frac{7}{4^m}=0.$ The sum of the series is

$($Simplify your answer.$)$

The series converges because it is a geometric series with The sum of the series is

B$.$

$($Simplify your answer.$)$

C$.$ The series diverges because $\underset{n}{lim}\frac{7}{4^m}0$ or fails to exist.

D$.$ The series diverges because it is a geometric series with $|r|1.$