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This contribution deals with the generalized convergent harmonic series with three periodically repeated numerators; i. e. with periodically repeated numerators , where . Firstly, it is derived that the only value of the coefficient , for which this series converges, is . Then the formula for the sum of this series is analytically derived. A relation for calculation the value of the constant from an arbitrary sum also follows from the derived formula. The obtained analytical results are finally numerically verified by using the computer algebra system Maple 15 and its basic programming language.

SUM OF GENERALIZED ALTERNATING HARMONIC SERIES WITH THREE PERIODICALLY REPEATED NUMERATORS