# Leibniz criterion

From Encyclopedia of Mathematics

*for convergence of an alternating series*

If the terms of an alternating series

decrease monotonically (, ) and tend to zero (), then the series converges; moreover, a remainder of the series,

has the sign of its first term and is less than it in absolute value. The criterion was established by G. Leibniz in 1682.

#### Comments

#### References

[a1] | K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990) |

**How to Cite This Entry:**

Leibniz criterion.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Leibniz_criterion&oldid=18694

This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article