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