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