Summation by Parts

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The indefinite sum of a product can often be computed efficiently using summation by parts. For this technique to work effectively, the function
must have a simple expression for its indefinite sum while
must have a simple expression for its difference. Summation by parts provides a discrete analog for integration by parts that is used in ordinary infinitesimal calculus. This Demonstration considers the case when
is a monomial in the summation variable
and
is either the sequence of harmonic numbers or the digamma function, both of which have simple differences.
Contributed by: Devendra Kapadia (March 2011)
Open content licensed under CC BY-NC-SA
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"Summation by Parts"
http://demonstrations.wolfram.com/SummationByParts/
Wolfram Demonstrations Project
Published: March 7 2011