RE: Tough Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg34292] RE: [mg34235] Tough Limit
- From: "DrBob" <majort at cox-internet.com>
- Date: Tue, 14 May 2002 04:10:02 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
Your method of looking at examples is fraught with danger. 10, 100, 1000, and 10000 are all even numbers. Had you used odd numbers, you'd have gotten a limit of -1. Had you used appropriate real numbers, you could have gotten any number between -1 and +1 as a limit. That's why the limit (as originally posed) does NOT exist, and Mathematica was right not to find one. In this thread we've changed the problem to (a) take the absolute value and (b) restrict n to integers. Together, those changes are sufficient to make the limit 1. But that's not the original problem (as stated). Maybe it IS the original problem as intended; I don't know. Bobby Treat -----Original Message----- From: RJMilazzo at aol.com [mailto:RJMilazzo at aol.com] To: mathgroup at smc.vnet.net Subject: [mg34292] Re: [mg34235] Tough Limit Dear Bob; I think I see where you went wrong, you expanded your series around 0. Where you should of expanded around infinity. Mathematica can not expand this problem around infinity. It is easy to see empirically that the limit goes to 1. Sqrt[n*Pi]*Binomial[-2^(-1), n] /. n -> {10., 100., 1000., 10000.} {0.9875829288261563, 0.9987507861261873, 0.9998750078180174, 0.999987500075049} James