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Zbl 0628.40002
Rath, D.
A note on series and sequences.
(English)
[J] Indian J. Pure Appl. Math. 18, 625-629 (1987). ISSN 0019-5588; ISSN 0975-7465/e

A classical theorem by Pringsheim asserts that if $(a\sb n)$ is nonnegative, nonincreasing and if $\sum a\sb n$ converges, then $na\sb n\to 0$, as $n\to \infty$. In this note, some extensions and improvements of this result are considered which are then used to derive some properties of hyperconvex sequences analogous to those for convex sequences.
MSC 2000:
*40A05 Convergence of series and sequences

Keywords: hyperconvex sequences

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