That infinite series was added in January 2010 by an anonymous user from IP address 69.133.204.190, who rather tenaciously added it three times, I think. One of them ( http://en.wikipedia.org/w/index.php?title=Golden_ratio&diff=prev&oldid=33555...) included a citation, to Brian Roselle, https://sites.google.com/site/goldenmeanseries/ a somewhat self-important-seeming diatribe claiming that "While investigating the Golden Mean, no equivalent infinite series was found that explicitely defined" it. I won't speculate on what Brian Roselle's IP address might or might not be. It's Wikipedia -- go ahead and improve the article, that's what it's all about... --Michael On Sun, Nov 27, 2011 at 10:59 PM, Bill Gosper <billgosper@gmail.com> wrote:
Can anyone motivate their rather grotesque choice of an infinite series (13/8 + a 1F0[1/4])? Hey, why not some zip?: Binomial[2 n, n] 1970299 Sum[----------------, {n, 0, Infinity}] n 1 62113250390420 - + ----------------------------------------------- 2 1762289
(The +1/2 can be replaced by a factor of a n + b in the summand, for some integers a and b.) Actually, you're unlikely to beat (from Finch's opus) the superfast (doubly exponential) 4 - Sum[1/Fibonacci[2^n], {n, 0,∞}]. In typical fashion, Mma knows this one, just to be impressive, but not that it telescopes, just to be useful. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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