The sum of the series of reciprocals of the quadratic polynomial with different negative integer roots

Abstract

This contribution, which is afollow-up to author’s paper[1] and [2] dealing with the sums of the series of reciprocals of some quadratic polynomials, deals with the series of reciprocals of the quadratic polynomials with different negative integer roots. We derive the formula for the sum of this series and verify it by some examples evaluated using the basic programming language of the CAS Maple 16.

Keywords

• sequence of partial sums, telescoping series, harmonic num- ber, computer algebra system Maple.