Difference between revisions of "Leibniz series"
From Encyclopedia of Mathematics
(Importing text file) |
m (TeX encoding is done) |
||
| Line 1: | Line 1: | ||
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. |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)</TD></TR></table> | ||
Revision as of 09:36, 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://encyclopediaofmath.org/index.php?title=Leibniz_series&oldid=29173
Leibniz series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Leibniz_series&oldid=29173
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article