Difference between revisions of "Fibonacci numbers"

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=Properties=
 
=Properties=
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[[Limit of consecutive quotients of Fibonacci numbers]]<br />
<strong>Theorem:</strong> The following series holds and converges for all $|x| \leq \dfrac{1}{\varphi}$, where $\varphi$ denotes the [[golden ratio]]:
 
$$\dfrac{x}{1-x-x^2} = \displaystyle\sum_{k=1}^{\infty} F_k x^k.$$
 
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<strong>Proof:</strong> proof goes here █
 
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=Videos=
 
=Videos=

Revision as of 23:27, 27 June 2016

The Fibonacci sequence is defined by $$F_{n+2}=F_n+F_{n+1}, \quad F_1=F_2=1.$$

Properties

Limit of consecutive quotients of Fibonacci numbers

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

External links

The Fibonacci Quarterly
"What interesting properties of the Fibonacci sequence can I share when introducing sequences?"

References