Answer
$R=4$ ; the interval of convergence is $[-4,4]$
Work Step by Step
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{x^{n+1}}{(n+1)^44^{n+1}}}{\frac{x^{n}}{(n)^44^{n}}}|$
$=|x|/4$
Hence, $R=4$ ; the interval of convergence is $[-4,4]$
