Faldo:
I think you misinterpreted FF's sequence; it is the square root of 1 plus the square root of (1 plus the square root of(1 plus etc.))). The square root of 1 plus the square root of one becomes the square root of 2, or 1.414+, and the increments become smaller and smaller as you add more extensions. So it has to converge somewhere rather than diverging to infinity, which it would do if it were the square root of 1 + (the square root of 1) + (the square root of 1). . . which is just another way of saying 1 plus 1 plus 1 all the way to infinity.
See
http://tinyurl.com/v0b2 which is pretty much the same thing as what FF set forth. I'm not as versed in this stuff as I may have been once, but it looks correct to me. I do wonder though why FF has discarded the negative solution to the quadratic equation, calling it an extraneous root. I don't know what that means and I would be loath to totally disregard it.
TEd
