**Way OT**
Dear lady,
Regarding your math question...
At one time I would have been able to prove the following, but no longer (without more thinking than I am willing to do).
However, I am virtually certain that: The ratios of two successive terms in any 'Fibonacci like' sequence converge to ~.618 (or ~1.618) where 'Fibonacci like' is defined as a sequence that begins with any two positive integers with each successive integer the sum of the previous two in the sequence.
However, all summation series do NOT converge to .618, or anything else for that matter. For example, the series that converges to pi (~3.1415927).
BTW, the .618 is (approximately) the famous Golden Mean (or Golden Ratio) found in nature and the works of man, including the construction of the Parthenon. It is more exactly expressed as
2/(1+sqrt(5)), if memory serves.
FWIW, the ratios of successive terms in a 'Fibonnaci like' tri-sequence, where a term is determined as the sum of the previous THREE terms, also converges, though not to .618.
Funny, I've been thinking about posting about IOM for months, never thought I'd post about mostly long-forgotten math.
dls |
