Fibonacci numbers: Difference between revisions
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The beginning of the sequence is thus: | The beginning of the sequence is thus: | ||
:<math>0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots</math> | :<math>0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots</math> | ||
The ratio <math> \frac {F_n}{F_{n+1}} \ </math> approaches the [[golden ratio]] as <math>n</math> approaches infinity. | |||
== Resources: == | == Resources: == | ||
Revision as of 08:47, 2 May 2020
In mathematics, the Fibonacci numbers, commonly denoted [math]\displaystyle{ F_n }[/math], form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,
- [math]\displaystyle{ F_0=0,\quad F_1= 1, }[/math]
and
- [math]\displaystyle{ F_n=F_{n-1} + F_{n-2}, }[/math]
for [math]\displaystyle{ n \gt 1 }[/math].
The beginning of the sequence is thus:
- [math]\displaystyle{ 0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots }[/math]
The ratio [math]\displaystyle{ \frac {F_n}{F_{n+1}} \ }[/math] approaches the golden ratio as [math]\displaystyle{ n }[/math] approaches infinity.