Difference between revisions of "Reciprocal Fibonacci constant"
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The reciprocal Fibonacci constant $\psi$ is | The reciprocal Fibonacci constant $\psi$ is | ||
| − | $$\psi = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{ | + | $$\psi = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F(k)}=3.35988566624317755\ldots,$$ |
| − | where $ | + | where $F(k)$ is is the $k$th [[Fibonacci numbers|Fibonacci number]]. |
| + | |||
| + | =Properties= | ||
| + | [[Fibonacci zeta at 1 is irrational|The reciprocal Fibonacci constant is irrational]]<br /> | ||
=See also= | =See also= | ||
| − | [[Fibonacci | + | [[Fibonacci numbers]]<br /> |
| + | [[Fibonacci zeta function]]<br /> | ||
=References= | =References= | ||
| − | + | * {{PaperReference|Sur la série des inverse de nombres de Fibonacci|1899|Edmund Landau|prev=Limit of quotient of consecutive Fibonacci numbers|next=findme}} | |
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 03:40, 25 June 2017
The reciprocal Fibonacci constant $\psi$ is $$\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
