# Math Help - convergent or divergent?

1. ## convergent or divergent?

$\sum\frac{k^{k/2}}{k!}$

I'm trying to figure out whether this is convergent or divergent..but the thing that is confusing me here is the $k^{k/2}$

2. Originally Posted by akhayoon
$\sum\frac{k^{k/2}}{k!}$

I'm trying to figure out whether this is convergent or divergent..but the thing that is confusing me here is the $k^{k/2}$
Note, $\left| \frac{n^{n/2}}{n!} \right|^{1/n} = \frac{\sqrt{n}}{(n!)^{1/n} } = \frac{1}{\sqrt{n}}\cdot \frac{n}{(n!)^{1/n}} \to 0$ because $(n!)^{1/n}/n \to e$. Thus, by root test this converges.