The sum of the telescoping series formed by reciprocals of the cubic polynomials with three different negative integer roots

Abstract

This paper deals with the sum of a special telescoping series and is a free follow-up to author’s preceding paper. The terms of this series are reciprocals of the cubic polynomial with three different negative integer roots. The main result of the paper is to derive a formula for the sum of this series. This formula uses the limit of the sequence of the partial sums and is expressed by harmonic numbers. After that the main result is verified by some examples using the basic programming language of the computer algebra system Maple 19.

Keywords

• sum of the series
• sequence of partial sums
• telescoping series
• harmonic number
• computer algebra system maple