On the Relation between the Convergence of a Series and its Summability by Cesaro's Means

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Authors

DOI:

https://doi.org/10.18311/jims/1924/17652

Abstract

In the first of a series of important papers communicated to the London Mathematical Society, Hardy proved the following:

THEOREM: If Σan is summable (C1) to sum s, and if

an = O(1/n),

then Σan converges to sum s.