[math-fun] A puzzle I read about
If you haven't seen this one before, it's worth a try: (Provenance to be provided with solution.) << For positive x<1, consider the alternating sum S(x) = x - x2 + x4 - x8 + x16 - x32 + - ... Does S(x) approach a limit as x approaches 1 from below, and if so what is this limit?
--Dan
I don't think its exactly the answer you want, but i think it's the answer you want (does that make sense)? S(x) = x - x^2 + x^4 - x^8 + x^16 - x^32 ... satisfies S(x) = x - S(x^2). Now substitute in x = 1, which gives S(1) = 1/2. OK, so its formal, what can I say.... ----- Original Message ----- From: <dasimov@earthlink.net> To: <math-fun@mailman.xmission.com> Sent: Wednesday, May 18, 2005 5:12 AM Subject: [math-fun] A puzzle I read about
If you haven't seen this one before, it's worth a try:
(Provenance to be provided with solution.)
<< For positive x<1, consider the alternating sum S(x) = x - x2 + x4 - x8 + x16 - x32 + - ... Does S(x) approach a limit as x approaches 1 from below, and if so what is this limit?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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dasimov＠earthlink.net -
David Wilson