The sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root

Abstract

This contribution is a follow-up to author’s previous published papers and deals with the sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root. We derive the formula for the sum of these series and verify it by some examples 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

• sum of the series
• telescoping series
• generalized harmonic number
• digamma function
• euler’s constant
• computer algebra system maple