ABOUT CONVERGENCE OF THE GENERALIZED HARMONIC SERIES WHEN THE SIGNS OF ITS SUMMANDS ARE CHANGED
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 1
Abstract
In this paper we study the question about convergence of the generalized harmonic series when the signs of its summands are changed. For this we consider the sequence of numbers where the sign is switched. The main result is the convergence criterion of a generalized harmonic series with changed signs in terms of the sign switching numbers. This criterion allows us to reduce the question of convergence to the study of a simpler, namely, sign alternating series. There are given several examples of the application of the obtained criterion. The most interesting was the example of a power growth of the sign switching numbers, because there is a transition to integer parts in the case when the exponent is not natural. Necessary and sufficient conditions for convergence are obtained, but the question is not solved in full, because these conditions do not coincide.
Authors and Affiliations
S. R. Voronkova
Keywords
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- DOI 10.18524/2519-206x.2018.1(31).134617
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