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

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{7(3x{)}^k}{2k}$

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

A$.$ The series converges only when $$

integers $or$ simplified fractions.$)$

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

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

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

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

$C.$ The series converges only when $x<mtext></mtext><mi></mi><mtext></mtext><mi>(</mi><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi>$ integers $or$ simplified fractions.$)$

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

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

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

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