Difference between revisions of "Binet's formula"
From specialfunctionswiki
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The following formula holds: | The following formula holds: | ||
$$F_n = \dfrac{\phi^n - (-\phi)^{-n}}{\sqrt{5}},$$ | $$F_n = \dfrac{\phi^n - (-\phi)^{-n}}{\sqrt{5}},$$ | ||
| − | where $F_n$ denotes a [[Fibonacci | + | where $F_n$ denotes a [[Fibonacci numbers|Fibonacci number]] and $\phi$ denotes the [[golden ratio]]. |
==Proof== | ==Proof== | ||
Revision as of 00:28, 24 May 2017
Theorem
The following formula holds: $$F_n = \dfrac{\phi^n - (-\phi)^{-n}}{\sqrt{5}},$$ where $F_n$ denotes a Fibonacci number and $\phi$ denotes the golden ratio.
