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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 179, Pages 78–80 (Mi into630)  

On the esàro convergence of numerical series

V. V. Timoshenko

Moscow State Pedagogical University

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

DOI: https://doi.org/10.36535/0233-6723-2020-179-78-80

Full text: PDF file (106 kB)
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UDC: 517.521
MSC: 4005, 4005, 40F05, 40G05

Citation: V. V. Timoshenko, “On the esàro 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. Ser. Sovrem. Mat. Pril. Temat. Obz., 179, VINITI, Moscow, 2020, 78–80

Citation in format AMSBIB
\Bibitem{Tim20}
\by V.~V.~Timoshenko
\paper On the es\`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. Ser. 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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