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.
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