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A theorem from the theory of infinite series. (Ein Satz aus der Theorie der unendlichen Reihen.) (German) JFM 28.0221.02

Beweis des Satzes: Damit die Reihe \(\sum\limits_1^\infty a_\nu\) convergirt, ist erforderlich und hinreichend, dass gleichzeitig \(\lim\limits_{\varrho=1}\sum\limits_1^\infty a_\nu\varrho^\nu\) existirt und dass \(\lim\limits_{n=\infty}\frac1n\sum\limits_1^n \nu a_\nu=0\) ist.

MSC:

40E05 Tauberian theorems
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References:

[1] Kronecker, Comptes rendus, T. 103, pag. 980.
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