Proving inequalities with Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg52491] Proving inequalities with Mathematica*From*: "Toshiyuki \(Toshi\) Meshii" <meshii at mech.fukui-u.ac.jp>*Date*: Mon, 29 Nov 2004 01:22:40 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Proving inequalities with Mathematica***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>