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===[[Fibonacci sequence]]=== | ===[[Fibonacci sequence]]=== | ||
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The '''Fibonacci sequence''' is a [[sequence]] of [[integer]]s in which the first and second terms are both equal to 1 and each subsequent term is the sum of the two preceding it. The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. | The '''Fibonacci sequence''' is a [[sequence]] of [[integer]]s in which the first and second terms are both equal to 1 and each subsequent term is the sum of the two preceding it. The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. | ||
The Fibonacci sequence can be written [[recursion|recursively]] as <math>F_1 = F_2 = 1</math> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>. This is the simplest nontrivial... [[Fibonacci sequence|[more]]] | The Fibonacci sequence can be written [[recursion|recursively]] as <math>F_1 = F_2 = 1</math> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>. This is the simplest nontrivial... [[Fibonacci sequence|[more]]] | ||
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Revision as of 22:56, 16 December 2007
Fibonacci sequence
This article was also a AoPSWiki word of the week
The Fibonacci sequence is a sequence of integers in which the first and second terms are both equal to 1 and each subsequent term is the sum of the two preceding it. The first few terms are
.
The Fibonacci sequence can be written recursively as
and
for
. This is the simplest nontrivial... [more]
.
and 
for 
. This is the simplest nontrivial... 
