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Ponder This

September 2006

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Ponder This Challenge:

Puzzle for September 2006.

Let f(n) be a function on the non-negative integers defined recursively as follows:

f(0)=1, f(n)=(1+(n*n-n)*f(n-1))/(n*n+1) for n > 0. So f(1)=1/2, f(2)=2/5 ...

This month's puzzle asks for you to determine the asymptotic behavior of f(n) as n -> infinity. In other words find a simple function g(x) such that f(n)/g(n) -> 1 as n -> infinity.


We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

  

Challenge: 09/07/2006 @ 10:30 AM EST
Solution: 10/02/2006 @ 10:00 AM EST
List Updated: 10/02/2006 @ 11:00 AM EST

People who answered correctly:

V. Balakrishnan (09.07.2006 @11:58:45 AM EDT)
Richard Mann (09.07.2006 @04:38:17 PM EDT)
Arthur Breitman (09.07.2006 @05:15:15 PM EDT)
Dan Dima (09.07.2006 @07:57:03 PM EDT)
Oleg Trott (09.08.2006 @01:08:46 AM EDT)
Michael Quist (09.08.2006 @01:12:09 AM EDT)
Aravind (09.08.2006 @04:33:53 AM EDT)
Frank Yang (09.08.2006 @10:42:16 AM EDT)
Dinesh Krithivasan (09.08.2006 @03:04:21 PM EDT)
David McQuillan (09.08.2006 @04:32:33 PM EDT)
Lizhao Zhang (09.08.2006 @09:04:46 PM EDT)
Alan Murray (09.09.2006 @01:12:40 AM EDT)
Wolf Mosle (09.09.2006 @01:58:56 PM EDT)
Jerold Lewandowski (09.09.2006 @05:55:42 PM EDT)
Didier Bizzarri (09.09.2006 @09:05:37 PM EDT)
Arjun Acharya (09.10.2006 @02:08:20 PM EDT)
Zhou Guang (09.10.2006 @10:52:47 PM EDT)
Vincent Vermaut (09.11.2006 @10:40:49 AM EDT)
Arvind L. (09.11.2006 @11:32:28 AM EDT)
Victor Popov (09.11.2006 @05:23:35 PM EDT)
S. Amghibech (09.11.2006 @08:15:17 PM EDT)
John Fletcher (09.12.2006 @01:25:22 PM EDT)
Paolo Massaro (09.12.2006 @03:47:42 PM EDT)
Emilio Schiavi (09.12.2006 @05:37:41 PM EDT)
John T. Robinson (09.12.2006 @07:10:07 PM EDT)
John Ritson (09.13.2006 @04:05:06 AM EDT)
Piotr Zielinski (09.13.2006 @05:27:54 PM EDT)
John Dalbec (09.13.2006 @07:50:17 PM EDT)
Wu Hao (09.13.2006 @09:34:43 PM EDT)
Luke Pebody (09.14.2006 @05:43:02 AM EDT)
Matthew Samuel (09.14.2006 @11:45:19 PM EDT)
Ariel Flat (09.14.2006 @05:40:52 PM EDT)
Lawrence Hon (09.15.2006 @06:13:17 AM EDT)
Phil Muhm (09.15.2006 @10:15:57 AM EDT)
Du Yang (09.17.2006 @02:55:50 AM EDT)
Se Kwon Kim (09.18.2006 @03:13:23 AM EDT)
Mingrui Wu (09.18.2006 @08:11:28 AM EDT)
Steven Noble (09.18.2006 @11:56:28 PM EDT)
Christian Blatter (09.19.2006 @06:23:03 AM EDT)
Dion Harmon (09.19.2006 @06:11:14 PM EDT)
Dave Parashar (09.20.2006 @09:39:11 AM EDT)
Yoav Raz (09.21.2006 @12:01:06 AM EDT)
Chris Shannon (09.22.2006 @12:02:17 AM EDT)
Joachim Ripken (09.22.2006 @07:46:46 AM EDT)
Oded Margalit (09.23.2006 @04:43:19 PM EDT)
Anatoly Morosov (09.26.2006 @11:28:21 AM EDT)
Ray Gregory (09.28.2006 @10:06:13 PM EDT)
Firat Solgun (09.29.2006 @05:23:02 PM EDT)
William Hasenplaugh (09.29.2006 @07:20:25 PM EDT)
Li Han (10.01.2006 @11:39:40 AM EDT)


Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.