Difference between revisions of "Fibonacci numbers"
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[http://matheducators.stackexchange.com/questions/2021/what-interesting-properties-of-the-fibonacci-sequence-can-i-share-when-introduci]<br /> | [http://matheducators.stackexchange.com/questions/2021/what-interesting-properties-of-the-fibonacci-sequence-can-i-share-when-introduci]<br /> | ||
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Revision as of 18:57, 24 May 2016
The Fibonacci sequence is defined by $$F_{n+2}=F_n+F_{n+1},F_1=F_2=1.$$
Contents
Properties
Theorem: The following series holds and converges for all $|x| \leq \dfrac{1}{\varphi}$, where $\varphi$ denotes the golden ratio: $$\dfrac{x}{1-x-x^2} = \displaystyle\sum_{k=1}^{\infty} F_k x^k.$$
Proof: proof goes here █
Videos
The Golden Ratio & Fibonacci Numbers: Fact versus Fiction
Doodling in Math: Spirals, Fibonacci, and Being a Plant (1 of 3)
Fibonacci mystery
See also
Golden ratio
Reciprocal Fibonacci constant
Lucas numbers
