Difference between revisions of "Limit of quotient of consecutive Fibonacci numbers"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\lim_{n \rightarrow \infty} \dfrac{F_{n+1}}{F_n}=\phi,$$ where $F_n$ denotes the Fibonacci sequence and $\phi$ deno...") |
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The following formula holds: | The following formula holds: | ||
$$\displaystyle\lim_{n \rightarrow \infty} \dfrac{F_{n+1}}{F_n}=\phi,$$ | $$\displaystyle\lim_{n \rightarrow \infty} \dfrac{F_{n+1}}{F_n}=\phi,$$ | ||
| − | where $F_n$ denotes the [[Fibonacci | + | where $F_n$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]] and $\phi$ denotes the [[golden ratio]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| − | * {{PaperReference|Sur la série des inverse de nombres de Fibonacci|1899|Edmund Landau|prev=Fibonacci | + | * {{PaperReference|Sur la série des inverse de nombres de Fibonacci|1899|Edmund Landau|prev=Fibonacci numbers|next=Reciprocal Fibonacci constant}} |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 00:27, 24 May 2017
Theorem
The following formula holds: $$\displaystyle\lim_{n \rightarrow \infty} \dfrac{F_{n+1}}{F_n}=\phi,$$ where $F_n$ denotes the $n$th Fibonacci number and $\phi$ denotes the golden ratio.
