Sums of Generalized Alternating Harmonic Series with Periodically Repeated Numerators (1,a) and (1,1,a)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F14%3A00521822" target="_blank" >RIV/60162694:G43__/14:00521822 - isvavai.cz</a>
Result on the web
<a href="http://vavtest.unob.cz/registr" target="_blank" >http://vavtest.unob.cz/registr</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Sums of Generalized Alternating Harmonic Series with Periodically Repeated Numerators (1,a) and (1,1,a)
Original language description
This paper deals with certain generalization of the alternating harmonic series ? the generalized harmonic series with periodically repeated numerators (1,a) and (1,1,a). Firstly, we show that the only one value of the numerator a of the first series, for which the series converges, is a = -1 and that its sum is ln 2. Further, we derive that the only one value of the numerator a of the second series, for which the series converges, is a = -2 and that its sum is ln 3. Finally, we verify this analyticallyobtained result and compute the sum of this series by using the computer algebra system Maple 15 and its basic programming language.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Mathematics, Information Technologies and Applied Sciences 2014 post-conference proceedings of selected papers extended versions
ISBN
978-80-7231-978-7
ISSN
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e-ISSN
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Number of pages
6
Pages from-to
83-88
Publisher name
University of Defence, Brno
Place of publication
Brno
Event location
Brno
Event date
Jan 1, 2014
Type of event by nationality
CST - Celostátní akce
UT code for WoS article
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