David,

Looking further at what you are trying to prove, its clear that, though you can have geometric sequences over the naturals, this kind of result will not be obtainable in that context.

As soon as you thing of them as series, things go awry, since non but the absolutely trivial ones converge.

So if you want to reason about these things then you will need real numbers and can best work from maths_egs.

However the leap from the kind of reasoning you have been doing to formal proof in analysis is very great (also, if it matters to you, this is no longer discreet mathematics!) and I would have thought that carrying through some arithmetic proofs would be a more manageable advance for you.

Roger

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