# Leibniz series

From Encyclopedia of Mathematics

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

The alternating series \begin{equation} 1-\frac13+\frac15-\frac17+\dots, \end{equation} 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://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