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MathGroup Archive 2004

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Re: Proving inequalities with Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52498] Re: Proving inequalities with Mathematica
  • From: Peter Pein <petsie at arcor.de>
  • Date: Tue, 30 Nov 2004 05:24:00 -0500 (EST)
  • References: <coeg10$rhf$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Toshiyuki (Toshi) Meshii wrote:

> Hi,
> 
> I was wondering whether Mathematica is useful for proving a problem of 
> inequality.
> My problem is as follows:
> 
> Let An and Bn (n=1,2,3...) be real sequences.
> Some characteristics of these sequences are known.
> 
> i) Abs[An+1/An] < 1
> ii) Abs[Bn+1/Bn] < 1
> iii) Sum[An, {1,Infinity}] = 0
> iv) Sum[An*Bn, {1, Infinity}] = alpha (note: a real number)
> 
> Then I want to prove with Mathematica that
> 0 < Abs[alpha] < Abs[A1*B1]
> 
> Does anyone have an idea?
> 
> -Toshi 
> 
Sorry Toshi, I can't imagine any sequence of real A_n with
|A_n + 1/A_n|<1

-- 
Peter Pein
10245 Berlin


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