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

Radovan Potucek


This paper deals with certain generalization of the alternating harmonic series - the generalized convergent harmonic series with periodically repeated numerators (a,b) and (a,a,b,b). Firstly, we find out the value of the numerators b of the first series, for which the series converges, and determine the formula for the sum s(a) of this series. Then we determine the value of the numerators b of the second series, for which this series converges, and derive the formula for the sum s(a,a) of this second series. Finally, we verify these analytically obtained results and compute the sums of these series by using the computer algebra system Maple 16 and its basic programming language.


harmonic series; alternating harmonic series; sequence of partial sums; computer algebra system Maple

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R. Potucek, Sums of Generalized Alternating Harmonic Series with Periodically Repeated Numerators (1,a) and (1,1,a). In: Mathematics, Information Technologies and Applied Sciences 2014 post-conference proceedings of selected papers extended versions. University of Defence, Brno, (2014),83-88. ISBN 978-8-7231-978-7.

R. Potucek, Sum of generalized alternating harmonic series with three periodically repeated numerators. Mathematics in Education, Research and Applications, Vol. 1, no. 2, (2015), 42-48. ISSN 2453-6881.

R. Potucek, Sum of generalized alternating harmonic series with four periodically repeated numerators. In: Proceedings of the 14th Conference on Applied Mathematics APLIMAT 2015. Slovak University of Technology in Bratislava, Publishing House of STU, Slovak Republic, (2015), 638-643.ISBN 978-80-227-4314-3.

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