EUDML

Let $\sum_{n = 1}^{\infty} a_{n}$ be a convergent series of positive real numbers. L. Olivier proved that if the sequence $(a_{n})$ is non-increasing, then $lim_{n \to \infty} n a_{n} = 0$ . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having $lim_{n \to \infty} n a_{n} = 0$ ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the $ℐ$ -convergence, that is a convergence according to an ideal $ℐ$ of subsets of $ℕ$ . Again, Olivier’s theorem is a consequence of...

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 8 of 8

Sur les demi-groupes de fractions

Demi-groupes de fractions et plongement d'un demi-groupe dans un groupe

Interprétation factorielle du nombre de classes dans les ordres des corps quadratiques

Characterization of simple orbit graphs.

Propriétés des demi-groupes de fractions

Propriétés des demi-groupes de fractions

Another way for associating a graph to a group

Some generalizations of Olivier's theorem