TITLE: Sum to closed form?
QUESTION [5 upvotes]: Is there a general method for removing a sum from an expression to produce a closed form?
For example I needed to "unroll" the following expression in a recent programming competition (as $k_1$ and $k_2$ are large) and couldn't do it...
$$ \sum_{w=2}^{k_1}\sum_{h=2}^{k_2}(w-1)(h-1) $$
Do I miss some discrete math training?  By what method would you go about solving this?  Is there a common textbook that would cover this?

REPLY [4 votes]: To answer the question you asked, there is not in general a method for converting a summation to closed form.  
However, the book Concrete Mathematics, by Graham, Knuth, and Patashnik, discusses the evaluation of sums in great detail, and is full of techniques for converting them to closed form. It is also extremely readable. If you have not yet read it, then yes, you have missed some essential discrete math training.