Geodesic
On the Сes\`aro convergence of numerical series
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 179 (2020), pp. 78-80.

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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
Mots-clés : convergence, Cesàro convergence. 
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V. V. Timoshenko. On the Сes\`aro convergence of numerical series. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 179 (2020), pp. 78-80. http://geodesic.mathdoc.fr/item/INTO_2020_179_a11/

[1] Khardi G., Raskhodyaschiesya ryady, IL, M., 1951