Answer
Radius of convergence is $e$.
Work Step by Step
We need to apply the Root Test to the series.
$L=\lim\limits_{n \to \infty} |a_n|^{1/n}=|x| \lim\limits_{n \to \infty} (\dfrac{n}{n+1})^n$
or, $=|x| \lim\limits_{n \to \infty} \dfrac{n+1}{8n+4}$
or, $=|x| \lim\limits_{n \to \infty} \dfrac{1}{e}$
or, $=\dfrac{1}{e}|x|$
Now, $\dfrac{1}{e}|x| \lt 1 \implies |x| \lt e$
Thus, the radius of convergence is $e$.
