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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 179, Pages 78–80
DOI: https://doi.org/10.36535/0233-6723-2020-179-78-80 (Mi into630) 		 
On the Сesàro convergence of numerical series

V. V. Timoshenko

Moscow State Pedagogical University
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DOI: https://doi.org/10.36535/0233-6723-2020-179-78-80
Abstract: The transition from a given series to the series of averaged sums of its terms is called the Cesàro procedure. In this paper, we construct a series for which $n$-multiple application of the Cesàro procedure gives divergent series whereas the $(n+1)$-multiple leads to a convergent series.
Keywords: series, convergence, Cesàro convergence.
Document Type: Article
UDC: 517.521
MSC: 40А05, 40В05, 40F05, 40G05
Language: Russian
Citation: V. V. Timoshenko, “On the Сesàro convergence of numerical series”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 179, VINITI, Moscow, 2020, 78–80
Citation in format AMSBIB
\Bibitem{Tim20}
\by V.~V.~Timoshenko
\paper On the Сes\`aro convergence of numerical series
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 179
\pages 78--80
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into630}
\crossref{https://doi.org/10.36535/0233-6723-2020-179-78-80}
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