# For what values of r does the sequence a_n = (nr)^n converge ?

$r = 0$
If $r \ne 0$ then when $n \ge \left\mid \frac{2}{r} \right\mid$ we have:
$\left\mid {\left(n r\right)}^{n} \right\mid \ge {2}^{n} \to \infty$ as $n \to \infty$