The sum of the reduced harmonic series generated by four primes determined analytically and computed by using CAS Maple

Authors

  • Radovan Potucek Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Kounicova 65, 662 10 Brno, Czech Republic

Keywords:

reduced harmonic series, sum of convergent infinite series, computer algebra system Maple.

Abstract

The paper deals with the reduced harmonic series generated by four primes. A formula for the sum of these convergent reduced harmonic series is derived. These sums (concretely 42 from all 12650 sums generated by four different primes smaller than 100) are computed by using the computer algebra system Maple 15 and its programming language, although the formula is valid not only for four arbitrary primes, but also for four integers. We can say that the reduced harmonic series generated by four primes (or by four integers) belong to special types of convergent infinite series, such as geometric and telescoping series, which sum can be found analytically by means of a simple formula.

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th Edition. Oxford University Press, London, 1975. ISBN 978-0-19-853310-7.

R. Potucek, Solving one in nite series problem using CAS Maple and analytically. Proceedings of International Conference Presenta-tion of Mathematics '11. Liberec: Faculty of Science, Humanities and Education of the Technical University of Liberec, Liberec, 2011, 107-112. ISBN 978-80-7372-773-4.

R. Potu cek, The sum of the reduced harmonic series generated by two primes determined analytically and computed by using CAS Maple. Zborn k vedeckych prac "Aplikovane ulohy v modernom vyucovan matematiky". Slovenska pol'nohospodarska univerzita v Nitre, 2012, 25-30. ISBN 978-80-552-0823-7.

R. Potucek, The sum of the reduced harmonic series generated by three primes determined analytically and computed by using CAS Maple. Zborn k vedeckych prac "Aplikacie matematiky { vstupna brana rozvoja matematickych kompetenci ". Slovenska pol'nohospodarska univerzita v Nitre, 2013, 84-89. ISBN 978-80-552-1047-6.

T. Rike, In nite Series (Berkeley seminary). Berkeley Math Circle, March 24, 2002, 6 pp.

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Published

2013-12-29

Issue

Vol. 25 (2013)

Section

Volume 25-2013

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