Thread: 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?



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!

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.