On 1/23/2012 5:02 AM, John VanSickle wrote:

> The rigorous proof that all such series will have a member-to-member
> ratio approaching phi will entail showing that for any two non-negative
> integers, A and B, with B>A, that the value of B/(A+B) is closer to phi
> (1.618~) than the value A/B.
>
> |A/B - phi| > |B/(A+B) - phi| for all A and B, 0 < A < B
>
> The full proof is left as an exercise for the interested student.

Although on second look it appears that you will have better results if 
you try proving this instead:

|B/A - phi| > |(A+B)/B - phi| for all A and B, 0 < A < B

Regards,
John

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