Difference between revisions of "Fibonacci numbers"
From specialfunctionswiki
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The Fibonacci sequence is defined by | The Fibonacci sequence is defined by | ||
| − | $$F_{n+2}=F_n+F_{n+1},F_1=F_2=1.$$ | + | $$F_{n+2}=F_n+F_{n+1}, \quad F_1=F_2=1.$$ |
=Properties= | =Properties= | ||
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=External links= | =External links= | ||
[http://www.fq.math.ca/ The Fibonacci Quarterly]<br /> | [http://www.fq.math.ca/ The Fibonacci Quarterly]<br /> | ||
| − | [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 "What interesting properties of the Fibonacci sequence can I share when introducing sequences?"]<br /> |
| + | |||
| + | =References= | ||
| + | * {{PaperReference|Sur la série des inverse de nombres de Fibonacci|1899|Edmund Landau|next=findme}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 23:24, 27 June 2016
The Fibonacci sequence is defined by $$F_{n+2}=F_n+F_{n+1}, \quad F_1=F_2=1.$$
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
External links
The Fibonacci Quarterly
"What interesting properties of the Fibonacci sequence can I share when introducing sequences?"
