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Proving inequalities with Mathematica


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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