Mathematics in Education, Research and Applications (MERAA), 2015(1), 2
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Received 2014-11-17 ǀ Accepted 2015-02-06 ǀ Published online 2015-11-16
DOI:http://dx.doi.org/10.15414/meraa.2015.01.02.42-48
SUM OF GENERALIZED ALTERNATING HARMONIC SERIES WITH THREE PERIODICALLY REPEATED NUMERATORS
Radovan Potůček
University of Defence, Brno, Czech Republic
Article Fulltext (PDF), 42–48
- This contribution deals with the generalized convergent harmonic series with three periodically repeated numerators, i.e. with periodically repeated numerators
(1a,b), where a,b ∈ ℝ. Firstly, it is derived that the only value of the coefficient b, for which this series converges, is b=-a-1.
Then the formula for the sum s(a) of this series is analytically derived. A relation for calculation the value of the constant a,b ∈ ℝ from an arbitrary
sum s(a) also follows from the derived formula. The obtained analytical results are finally numerically verified by using the computer algebra system Maple 15 and its basic
programming language.
- Keywords: harmonic series, alternating harmonic series, geometric series, sum of the series
- JEL Classification: I30