Saturday, March 17, 2007

 

1/4 + 1/16 + 1/64 + 1/256 + · · ·


In mathematics, the infinite series 1/4 + 1/16 + 1/64 + 1/256 + ... is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250-200 BC. Its sum is 1/3.

References: Shawyer, Bruce and Bruce Watson (1994). Borel's Methods of Summability: Theory and Applications. Oxford UP. ISBN 0-19-853585-6., Stein, Sherman K. (1999). Archimedes: What Did He Do Besides Cry Eureka?. MAA. ISBN 0883857189, Ajose, Sunday and Roger Nelsen (June 1994). "Proof without Words: Geometric Series". Mathematics Magazine 67 (3): 230, Mabry, Rick (February 1999). "Proof without Words: 1⁄4 + (1⁄4)2 + (1⁄4)3 + · · · = 1⁄3". Mathematics Magazine 72 (1): 63; Text of Quadrature of the Parabola with commentary. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "1/4 + 1/16 + 1/64 + 1/256 + · · ·". This entry is a fragment of a larger work. Link may die if entry is finally removed or merged.

# posted by Cliff Pickover @ 6:58 AM
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