THE SUM OF THE SERIES OF RECIPROCALS OF THE CUBIC POLYNOMIALS WITH THREE DIFFERENT NEGATIVE INTEGER ROOTS

摘要

This contribution is a follow-up to four author's previous papers and deals with the sum of the series of reciprocals of the cubic polynomials with three different negative integer roots. We derive the formula for the sum of these series, state two special cases of this formula and verify it by some examples using the basic programming language of the computer algebra system Maple 19.