Many thanks for that background. Well, I don't need a tug-of-war with some crank, especially when there is so much to be done for the Dragon Curve page. Hey, to go along with ChebyshevU[n, I/2]/I^n == Fibonacci[n + 1] I just rediscovered Hypergeometric2F1[1/2 - n/2, 1 - n/2, 3/2, 5]*n/2^(n - 1) == Fibonacci[n] which terminates after n/2 terms. No sqrts. --rwg (Here's the zippy golden ratio without the +1/2: Sum[(((50250675141714*n + 100501350283429/2)* Binomial[2*n, n])/((n + 1)*62113250390420^n)), {n, 0, Infinity}]/31056625195210 Now we need a theological argument that this is the One True Series.) --------------------- 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 Kleber