Mathematics in Education, Research and Applications (MERAA), 2017(3), 1
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Published online 2017-12-04
DOI:http://dx.doi.org/10.15414/meraa.2017.03.01.17-23
The sum of the series of reciprocals of the quadratic polynomials with purely imaginary conjugate roots
Radovan Potůček
University of Defence, Brno, Czech Republic
Article Fulltext (PDF), pp. 17–23
- This contribution, which is a follow-up to author's papers dealing with the sums of the series of reciprocals of quadratic
polynomials with different positive integer roots, different negative integer roots, and one negative and one positive integer root, deals
with the sum of the series of reciprocals of the quadratic polynomials with purely imaginary conjugate roots. We derive the formula for the
sum of these series and verify it by some examples evaluated using the basic programming language of the computer algebra system Maple 16.
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: sum of the series, harmonic number, purely imaginary conjugate roots, hyperbolic cotangent, computer algebra system Maple
- JEL Classification: I30