The sum of the reduced harmonic series generated by four primes determined analytically and computed by using CAS Maple

Radovan Potucek

Abstract


The paper deals with the reduced harmonic series generated by four primes. A formula for the sum of these convergent reduced harmonic series is derived. These sums (concretely 42 from all 12650 sums generated by four different primes smaller than 100) are computed by using the computer algebra system Maple 15 and its programming language, although the formula is valid not only for four arbitrary primes, but also for four integers. We can say that the reduced harmonic series generated by four primes (or by four integers) belong to special types of convergent infinite series, such as geometric and telescoping series, which sum can be found analytically by means of a simple formula.

Keywords


reduced harmonic series, sum of convergent infinite series, computer algebra system Maple.

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References


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R. Potucek, The sum of the reduced harmonic series generated by three primes determined analytically and computed by using CAS Maple. Zborn k vedeckych prac "Aplikacie matematiky { vstupna brana rozvoja matematickych kompetenci ". Slovenska pol'nohospodarska univerzita v Nitre, 2013, 84-89. ISBN 978-80-552-1047-6.

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.