In the same vein as this question
Striking applications of integration by parts
I'd also like to have a list of some good applications of the discrete version: summation by parts.
2026-03-25 18:56:28.1774464988
Striking applications of summation by parts
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Summation by parts is used to prove Abel's Theorem, and is also used in the Cauchy Criterion when testing for convergence.
Additionally, the following paper given here proves to be rather interesting.
Summation by parts also find many application in recreational mathematics such as IMO questions.