How would I determine and demonstrate whether or not the following series converges or diverges for a selected (arbitrary) real value for x:

?

I've found clearly that it diverges for any x of the form with m and k being integers. I've also found that it diverges for . However, I don't know if it diverge for all x (as I suspect), or if there are real values of x for which the series converges. How do I find out conclusively?

--Kevin C.