Answer
$R=k^{k}$
Work Step by Step
Let $a_{n}=\frac{(n!)^{k}x^{n}}{(kn)!}$, then
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{((n+1)!)^{k}x^{n+1}}{(k(n+1))!}}{\frac{(n!)^{k}x^{n}}{(kn)!}}|$
$=|x|(\frac{1}{k})^{k}$
$=|x|(\frac{1}{k})^{k}\lt 1$
Hence, $R=k^{k}$