The sum of the series of reciprocals of the quadratic polynomial with different negative integer roots

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.v30i1.12

Keywords:

sequence of partial sums, telescoping series, harmonic num- ber, computer algebra system Maple.

Abstract

This contribution, which is afollow-up to author’s paper[1] and [2] dealing with the sums of the series of reciprocals of some quadratic polynomials, deals with the series of reciprocals of the quadratic polynomials with different negative integer roots. We derive the formula for the sum of this series and verify it by some examples evaluated using the basic programming language of the CAS Maple 16.

References

R. Potucek, The sums of the series of reciprocals of some quadratic polynomials. In: Proceedings of AFASES 2010, 12th International Conference ”Scientific Research and Education in the Air Force” (CD-ROM). Brasov, Romania, 2010, p. 1206-1209. ISBN 978-973-8415-76-8.

R. Potucek, The sum of the series of reciprocals of the quadratic polynomials with double non-positive integer root. In: Proceedings of the 15th Conference on Applied Mathematics APLIMAT 2016. Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava, 2016, p. 919-925. ISBN 978-80-227-4531-4.

Wikipedia contributors: Harmonic number. Wikipedia, The Free Encyclopedia, [online], [cit.2016-09-01]. Available from: https://en.wikipedia.org/wiki/Harmonic number.

E.W. Weisstein, Harmonic Number. From MathWorld – A Wolfram Web Resource, [online], [cit.2016-09-01]. Available from: http://mathworld.wolfram.com/HarmonicNumber.html

A.T. Benjamin, G.O. Preston, and J.J. Quinn, A Stirling Encounter with Harmonic Numbers. Mathematics Magazine 75 (2), 2002, p. 95–103, [online], [cit.2016-09-01]. Available from: ttps://www.math.hmc.edu/∼benjamin/papers/harmonic.pdf

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Published

2016-06-16

Issue

Vol. 30 (2016)

Section

Volume 30-2016

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