Difference between revisions of "Reciprocal Fibonacci constant"

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(Created page with "The reciprocal Fibonacci constant $\psi$ is $$\psi = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_k},$$ where $F_k$ is is the $k$th term of the Fibonacci sequence. =Refer...")
 
 
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The reciprocal Fibonacci constant $\psi$ is  
 
The reciprocal Fibonacci constant $\psi$ is  
$$\psi = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_k},$$
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$$\psi = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F(k)}=3.35988566624317755\ldots,$$
where $F_k$ is is the $k$th term of the [[Fibonacci sequence]].
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where $F(k)$ is is the $k$th [[Fibonacci numbers|Fibonacci number]].
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=Properties=
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[[Fibonacci zeta at 1 is irrational|The reciprocal Fibonacci constant is irrational]]<br />
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=See also=
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[[Fibonacci numbers]]<br />
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[[Fibonacci zeta function]]<br />
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=References=
 
=References=
[https://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constant]
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* {{PaperReference|Sur la série des inverse de nombres de Fibonacci|1899|Edmund Landau|prev=Limit of quotient of consecutive Fibonacci numbers|next=findme}}
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[[Category:SpecialFunction]]

Latest revision as of 03:40, 25 June 2017

The reciprocal Fibonacci constant $\psi$ is $$\psi = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F(k)}=3.35988566624317755\ldots,$$ where $F(k)$ is is the $k$th Fibonacci number.

Properties

The reciprocal Fibonacci constant is irrational

See also

Fibonacci numbers
Fibonacci zeta function

References