How to show this series is divergent?

[KFC]

I got a series in the following form

$$\sum_{k=0}^\infty\dfrac{k!}{c^{2(k-1)}}$$

where c is arbritary complex constant, how can I show this series is divergent?

Thanks

 

[Ben Niehoff]

You have a factorial on top. It looks fairly obvious to me.

If it's not obvious to you, try a ratio test.

 

[HallsofIvy]

Yep, ratio test.