I am puzzled by the following infinite product:(adsbygoogle = window.adsbygoogle || []).push({});

Let B > A

A - B = [A^(1/2) + B^(1/2)] * [A^(1/2) - B^(1/2)]

= [A^(1/2) + B^(1/2)] * [A^(1/4) + B^(1/4)] * [A^(1/4) - B^(1/4)]

=[A^(1/2) + B^(1/2)] * [A^(1/4) + B^(1/4)] * [A^(1/8) + B^(1/8)] * [A^(1/8) - B^(1/8)]

etc.

Continuing the obvious expansion into an infinite product produces a sequence of terms none of which are negative. However, since B > A then A - B is a negative value. How can a infinite product of terms greater than zero produce a negative value? Surely there is a "simple" explanation.

Thanks for any comments.

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# A question about an infinite product

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