Namespaces
Variants
Actions

Dirichlet criterion (convergence of series)

From Encyclopedia of Mathematics
Revision as of 17:03, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

If a sequence of real numbers monotonically tends to zero, and the sequence of partial sums of the series is bounded (the terms of this series may also be complex), then the series converges. Established by P.G.L. Dirichlet [1].

References

[1] P.G.L. Dirichlet, J. de Math. (2) , 7 (1862) pp. 253–255


Comments

See also Dedekind criterion (convergence of series).

How to Cite This Entry:
Dirichlet criterion (convergence of series). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_criterion_(convergence_of_series)&oldid=30914
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article