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
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