The Sums of the Series of Reciprocals All the Triangular and All the Square Numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F10%3A00425214" target="_blank" >RIV/60162694:G43__/10:00425214 - 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
The Sums of the Series of Reciprocals All the Triangular and All the Square Numbers
Original language description
This contribution deals with triangular and square numbers. The sums of the series of their reciprocal values, as the sums of the reduced harmonic series, are derived. In the introductory part basic properties of these figurate numbers and relations between them are presented. In the major part the sums of the series of reciprocals the all triangular and square numbers are studied. These series present convergent series. The sum of the series of reciprocals the all triangular numbers is derived as the number 1. The sum of the series of reciprocals the all square numbers is the value zeta(2) = pi^2/6 = 1.645 of the Riemann zeta function zeta(s). The contribution can be an inspiration for teaching the topic Infinite series or as a subject matter for workwith talented students.
Czech name
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Czech description
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Zborník príspevkov 7. žilinskej didaktickej konferencie s medzinárodnou účasťou DIDZA, Fakulta prírodných vied, Žilinská univerzita v Žilině (CD-ROM)
ISBN
978-80-554-0216-1
ISSN
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e-ISSN
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Number of pages
8
Pages from-to
112-119
Publisher name
Fakulta prírodných vied, Žilinská univerzita v Žilině
Place of publication
Žilina, Slovakia
Event location
Žilina, Slovakia
Event date
Jan 1, 2010
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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