Math Help - Sum of a simple series

1. Sum of a simple series

Hi everybody! Problem: I don't know how to find an explicit form for this sum, anyone can help me?

$\sum_{k=-\infty}^{+\infty}\frac{1}{|x-kx_0|}$

here the calculations I made, but don't bring me anywhere:

https://dl.dropbox.com/u/8281720/SAM_1625.JPG

and my prof's version (I'm not sure he could be so quick on the absolute value)

https://dl.dropbox.com/u/8281720/photo.JPG

Thanks!

2. Re: Sum of a simple series

The sum is invariant under a transformation x -> x+n*x0 with integer n, therefore you can assume 0 < x < x0 (not equal, as the sum would not be well-defined then).

However, I do not see how this sum can converge at all - it is like two sums over (positive) 1/n, which have a logarithmic divergence.