# Difference between revisions of "Leibniz series"

From Encyclopedia of Mathematics

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The alternating series | The alternating series | ||

\begin{equation} | \begin{equation} |

## Revision as of 10:51, 12 December 2012

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

[a1] | 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=29174

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