Summation by parts

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation of certain types of sums. The rule states:

Suppose and are two sequences. Then,

Using the difference operator, it can be stated as more succinctly as

as an analogue to the integration by parts formula,

The summation by parts formula is sometimes called Abel's lemma.

External link

• "Abel's lemma" article at PlanetMath.org