Sums of generalized convergent harmonic series with eight periodically repeated numerators

Abstract

This contribution deals with the generalized convergent harmonic series with eight periodically repeated numerators and it is a follow-up to author’s papers dealing with the generalized alternating harmonic series with two up to seven periodically repeated numerators. It is derived the only expression of the last numerator depending on preceding numerators for which this series converges. Then the formula for the sum of this series is analytically derived. This analytical result is numerically verified by using the CAS Maple 16.

Keywords

• alternating harmonic series, geometric series, sum of the se- ries, CAS Maple.