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.
|[a1]||K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)|
Leibniz criterion. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Leibniz_criterion&oldid=18694