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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


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