Mathematics in Education, Research and Applications (MERAA), 2016(2), 1
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Received 2016-04-18 ǀ Accepted 2016-06-02 ǀ Published online 2016-10-30
DOI:http://dx.doi.org/10.15414/meraa.2016.02.01.15-21
The sum of the series of reciprocals of the quadratic polynomials with double positive integer root
Radovan Potůček
University of Defence, Brno, Czech Republic
Article Fulltext (PDF), pp. 15–21
- This contribution, which is a follow-up to author's papers, deals with the series of reciprocals of the quadratic polynomials
with double positive integer root. The formula for the sum of this kind of series expressed by means of harmonic numbers are derived and verified by
several examples evaluated using the basic programming language of the computer algebra system Maple 16. There is stated another formula using generalized
harmonic numbers, too. This contribution can be an inspiration for teachers of mathematics who are teaching the topic Infinite series or as a subject matter for work with talented students.
- Keywords: telescoping series, harmonic numbers, CAS Maple, Riemann zeta function
- JEL Classification: I30