Leibniz series

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2020 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.


[Kn] K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)
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Leibniz series. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article