Leibniz series

2010 Mathematics Subject Classification: Primary: 40A05 [MSN][ZBL]

The alternating series $$1-\frac13+\frac15-\frac17+\dots,$$ which converges to $\pi/4$. It was considered by G. Leibniz in 1673–1674.

References

 [Kn] K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)
How to Cite This Entry:
Leibniz series. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Leibniz_series&oldid=30912
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article