Abstract
The transition from a given series to the series of arithmetic means 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.
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References
G. H. Hardy, Divergent Series, Chelsea, New York (1991).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 179, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.
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Timoshenko, V.V. On the Cesàro Convergence of Numerical Series. J Math Sci 276, 428–429 (2023). https://doi.org/10.1007/s10958-023-06760-z
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DOI: https://doi.org/10.1007/s10958-023-06760-z