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