Statement
Suppose and are two sequences. Then,
Using the forward difference operator, it can be stated more succinctly as
Note that summation by parts is an analogue to the integration by parts formula,
Note also that although applications almost always deal with convergence of sequences, the statement is purely algebraic and will work in any field. It will also work when one sequence is in a vector space, and the other is in the relevant field of scalars.
Read more about this topic: Summation By Parts
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