Difference between revisions of "Leibniz series"
From Encyclopedia of Mathematics
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The alternating series | The alternating series | ||
| − | + | \begin{equation} | |
| − | + | 1-\frac13+\frac15-\frac17+\dots, | |
| − | + | \end{equation} | |
| − | which converges to | + | which converges to $\pi/4$. It was considered by G. Leibniz in 1673–1674. |
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====References==== | ====References==== | ||
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| + | |valign="top"|{{Ref|Kn}}|| K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990) | ||
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Latest revision as of 20:19, 9 December 2013
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.
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=14430
Leibniz series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Leibniz_series&oldid=14430
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article