Use the Ratio Test or the Root Test to determine the values of $x$ for which the series converges.

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{5(4x{)}^k}{3k}$

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

A$.$ The series converges only when $x=($Type an integer or a simplified fraction. Use a comma to separate answers as needed.$)$

B$.$ The series converges only when $x<mtext></mtext><mi></mi><mtext></mtext><mi>(</mi>$Type integers or simplified fractions.$)$

C$.$ The series converges only when $xxq,(Type$ integers $or$ simplified fractions.$)$

$F.$ The series converges for all $x.$

$q,G.$ The series diverges for all $x.(Type$ integers $or$ simplified fractions.$)$

$D.$ The series converges only when $x(Type$ integers $or$ simplified fractions.$)$

$E.$ The series converges only when $(Type$ integers $or$ simplified fractions.$)$

$F.$ The series converges for all $x.$

$q,G.$ The series diverges for all $x.$