How to show this series is divergent?

KFC

488
4
I got a series in the following form

[tex]\sum_{k=0}^\infty\dfrac{k!}{c^{2(k-1)}}[/tex]

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

Thanks
 

Ben Niehoff

Science Advisor
Gold Member
1,855
156
You have a factorial on top. It looks fairly obvious to me.

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

HallsofIvy

Science Advisor
41,626
821
Yep, ratio test.
 

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