Show that $r^{\ln(n)} = n^{\ln(r)}$. Then determine the values of $r$ (with $r>0$) for which the series $\sum\limits_{n=1}^{\infty} r^{\ln(n)}$ converges.

$r$ must be in the interval
(Give your answer as an appropriate interval: e.g., if your answer requires $r > 7$, enter (7,infinity), or if you need $3 \le r< 7$, enter [3,7). )