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

Radovan Potucek

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.

Keywords


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

Full Text:

PDF

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




DOI: http://dx.doi.org/10.23755/rm.v30i1.12

Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Radovan Potucek

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.