On 9/11/06, Daniel Asimov <dasimov@earthlink.net> wrote:
Btw, on his website, Noam Elikies asks what the limit is of the infinite series g(x) = x - x^2 + x^4 - x^8 + . . . +- x^(2^k) -+ . . .
(which converges for |x| < 1) as x -> 0-. It's a cool problem to let students try to guess the answer just using calculators.
Good point, Richard, and the limit as x -> 0 is not that interesting,
either.
I posted the wrong question, yet another mistake created by undue
haste.
*****The question of interest is: "What happens to g(x) as x -> 1-
?"
--Dan
Plot g(1-exp(-x)). For x > 6, the graph becomes periodic. g(x) ~ 0.5 + 0.027 sin(2 pi (x - 0.526) /1.385). Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com