[Graeme and David]:
This means the sequence diverges
... yes, I'm afraid you're both right -- simplification or not, the seq diverges :-( Best and thanks, É. -----Message d'origine----- De : math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com [mailto:math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com] De la part de David Wilson Envoyé : mardi 21 août 2007 2:45 À : math-fun Objet : Re: [math-fun] Look and divide There are at least [10^(n-1)/n] fractions with numerator n, the smallest of which is at least [n/(10^(n-1))+n-1)]. This means that the fractions with numerator n add up to at least 10^(n-1)/(10^(n-1)+n-1), which approaches 1 for any n. This means the sequence diverges. ----- Original Message ----- From: "Eric Angelini" <Eric.Angelini@kntv.be> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Monday, August 20, 2007 12:13 PM Subject: [math-fun] Look and divide Hello Math fun, read any fraction hereunder as: (quantity of digits used by the last term) ______________________________________________ (quantity of digits used in the sequence so far) Does the sum of all terms converge towards a precise number? (Sorry if this is old hat) Best, É. 0 1/1 2/3 2/5 2/7 2/9 2/11 3/14 3/17 3/20 3/23 3/26 3/29 ... (Example: the last fraction reads: "The preceding fraction uses 3 digits and the digits used so far in the sequence are 29") _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.484 / Virus Database: 269.12.0/961 - Release Date: 8/19/2007 7:27 AM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun