Use the Root Test to determine the convergence or divergence of the series. sum_{n=1}^infty(frac{n}{500})^n

Given: $\sum _{n=1}^{\mathrm{\infty }}(\frac{n}{500}{)}^n$
Root test: Suppose we have the series $\sum a_n$, Define $L=\underset{n\to \mathrm{\infty }}{lim}\sqrt[n]{|a_n|}=\underset{n\to \mathrm{\infty }}{lim}|a_n{|}^{\frac{1}{n}}$
Then,
1) If $L<1$, the series is absolutely convergent (and hence convergent).
2) If $L>1$, the series is divergent.
3) If $L=1$, the series may be divergent, conditionally convergent, or absolutely convergent.
Now consider,
$a_n=(\frac{n}{500}{)}^n$
$L=\underset{n\to \mathrm{\infty }}{lim}|(\frac{n}{500}{)}^n{|}^{\frac{1}{n}}$
$=\underset{n\to \mathrm{\infty }}{lim}\frac{n}{500}$
$=\frac{\mathrm{\infty }}{500}$
$=\mathrm{\infty }>1$
As $L>1$, by the Root Test the series is divergent.