Prove that the sequence formed from the ratios of consecutive elements in the Fibonacci sequence converges to?

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Prove that the sequence formed from the ratios of consecutive elements in the Fibonacci sequence converges to?

the golden mean.

2006-09-21 13:57:55 · 2 answers · asked by ttybrs10 1 in Science & Mathematics ➔ Mathematics

2 answers

b/a = (a+b)/b is the ratio.

therefore b^2 = a^2 +ab

b^2 - ab - a^2 = 0

solve this equation using the quadratic formula, and you get:

(1 +- sqrt(5))/2, i.e. the Golden Ratio

2006-09-21 14:05:09 · answer #1 · answered by Anonymous · 1⤊ 0⤋

I assume you mean the mathematical concept of the "golden ratio", not the philosophical "golden mean." Check the wiki link for an explanation.

http://en.wikipedia.org/wiki/Golden_ratio

2006-09-21 21:05:53 · answer #2 · answered by Dave 5 · 0⤊ 0⤋