Sums of generalized convergent harmonic series with eight periodically repeated numerators

Authors

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

DOI:

https://doi.org/10.23755/rm.v28i1.24

Keywords:

alternating harmonic series, geometric series, sum of the se- ries, CAS Maple.

Abstract

This contribution deals with the generalized convergent harmonic series with eight periodically repeated numerators and it is a follow-up to author’s papers dealing with the generalized alternating harmonic series with two up to seven periodically repeated numerators. It is derived the only expression of the last numerator depending on preceding numerators for which this series converges. Then the formula for the sum of this series is analytically derived. This analytical result is numerically verified by using the CAS Maple 16.

References

Potucek R.: Sum of generalized alternating harmonic series with periodically repeated numerators (1,a) and (1,1,a). In: Proceedings of Conference Matematika, Informaˇ cn´ ı Technologie a Aplikované vˇ edy MITAV 2014, Brno: University of Defence, 2014, p. 171-177. ISBN 978-80-7231-961-9.

Potucek R.: Sum of generalized alternating harmonic series with three periodically repeated numerators. Mathematics in Education, Research and Applications, Slovenská pol’nohospodárska univerzita v Nitre, 2015, p. 42-48. ISSN 2453-6881.

Potucek R.: Sum of generalized alternating harmonic series with four periodically repeated numerators. In: Proceedings of the 14th Conference on Applied Mathematics APLIMAT 2015. Bratislava, Slovak University of Technology in Bratislava, 2015, p. 638-643. ISBN 978-80-2274-314-3.

Potucek R.: Sum of generalized alternating harmonic series with five periodically repeated numerators. In: Proceedings of reviewed contributions on CD-ROM, XXXIII International Colloquium on the Management of Educational Process, University of Defence, Brno, 2015, p. 33-40. ISBN 978-80-7231-995-4.

Potucek R.: Sum of generalized alternating harmonic series with six periodically repeated numerators. In: Proceedings of Conference Matematika, Informaˇ cn´ ı Technologie a Aplikované vˇ edy MITAV 2015, University of Defence, Brno, 2015, p. 42-49. ISBN 978-80-7231-998-5.

Potucek R.: Sum of generalized alternating harmonic series with seven periodically repeated numerators. In: 9. didaktická konference s mezinárodnı úcastı – sbornık abstraktu a prıspevku. Masarykova univerzita, Brno, 2015, p. 43-52. ISBN 978-80-2107-814-7.

Husek M., Pyrih P.: Matematická anal´ yza [online]. [cit.2015-03-21]. Available from: http://matematika.cuni.cz/dl/analyza/25-raf/lekce25-rafpmax.pdf.

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Published

2015-07-01

Issue

Vol. 28 (2015)

Section

Volume 28-2015

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