Computing the radius of convergence of $\sum_{k=0}^{\infty}k^kx^k$

Question

In order to compute the radius of convergence of $$ \sum_{k=0}^{\infty}k^k x^k, $$ I computed $$ \lim_{k\to\infty}\left\lvert\frac{k^k}{k^{k+1}}\right\rvert=\lim_{k\to\infty}\frac{1}{k}=0. $$

Hence, the radius of convergence is $r=0$?