Sums of Generalized Harmonic Series with Periodically Repeated Numerators (a,b) and (a,a,b,b)

Abstract

This paper deals with certain generalization of the alternating harmonic series ? the generalized convergent harmonic series with periodically repeated numerators (a,b) and (a,a,b,b). Firstly, we ?nd out the value of the numerators bofthe?rstseries, forwhichtheseriesconverges, anddetermine the formula for the sum s(a) of this series. Then we determine the value of the numerators b of the second series, for which this series converges, and derive the formula for the sum s(a,a) of this second series. Finally, we verify these analytically obtained results and compute the sums of these series by using the computer algebra system Maple 16 and its basic programming language.

Keywords

• harmonic series
• alternating harmonic series
• sequence of partial sums
• computer algebra system Maple