11 Sep
2006
11 Sep
'06
4:42 p.m.
Richard Guy asks: << Is there any difficulty as x --> 0- or 0+ ? I thought that the interesting question is x --> 1- R. . . . On 9/10/06, 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