Answer
$e$
Work Step by Step
Let us apply the Root Test to the given series.
In order to find the radius of convergence, we have:
$l=\lim\limits_{n \to \infty} |a_n|^{(1/n)}=|x| \lim\limits_{n \to \infty} (\dfrac{n}{n+1})^n \\=|x| \lim\limits_{n \to \infty} \dfrac{1}{e} \\=\dfrac{1}{e}|x|$
So, $\dfrac{1}{e}|x| \lt 1$ and $|x| \lt e$
Thus, the radius of convergence is: $e$
