RE: Tough Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg34257] RE: [mg34235] Tough Limit
- From: "DrBob" <majort at cox-internet.com>
- Date: Sun, 12 May 2002 03:26:01 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
Your expression doesn't tend to a constant, but is in fact unbounded:
Series[Binomial[-1/2,n],{n,0,2}]
evaluates to (essentially)
1 - 1.38629 n + O[n]^2
and your expression's asymptotic behaviour is
Series[Binomial[-1/2,n]Sqrt[n Pi],{n,0,2}]
Sqrt[n Pi] - 2.45714 n^(3/2) + O[n]^5/2
Bobby Treat
-----Original Message-----
From: RJMilazzo [mailto:rjmilazzo at aol.com]
To: mathgroup at smc.vnet.net
Subject: [mg34257] [mg34235] Tough Limit
Can anyone suggest how I can use Mathematica to get the following limit:
limit ( Binomial [-1/2 ,n ] * Sqrt[ n* Pi ] ) as n-> Infinity
I have tried both Calculus`Limit` and the standard Limit functions. I
can
verify with NLimit that this limit equals approximately 1. I don't
think that
this is rigorous enough for a proof.
Thanks
James
rjmilazzo at aol.com