I'm using the following book as reference:

** Walter G. Kelly and Allan C. Peterson *Difference Equations* Second Edition, Harcourt Academic Press, 2001. **

I gather from the book and from research that it's generally difficult to find sums involving fractions with complicated denominators.

I'd like to know what is known about these sums. One thing that particularly springs up is what techniques generally work well for finding these sums. The book lists some general properties of indefinite sums, and some properties seem to go well with products, but don't seem to work well with fractions. I wonder if there is some general way to organize complicated fractions so that they are easy to sum.