The sum of the series of reciprocals of the cubic polynomials with triple non-positive integer root

Abstract

This contribution, which is a follow-up to author’s paper [1] dealing with the sums of the series of reciprocals of some quadratic polynomials, deals with the series of reciprocals of the cubic polynomials with triple non-positive integer root. Three formulas for the sum of this kind of series expressed by means of harmonic numbers are derived and presented, together with one approximate formula, and verified by several examples evaluated using the basic programming language of the computer algebra system Maple 16. This contribution can be an inspiration for teachers 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.