Difference between revisions of "Fibonacci sequence"
m (proofreading) |
|||
| Line 1: | Line 1: | ||
| − | The '''Fibonacci sequence''' is a [[sequence]] of [[integer]]s in which the first and second term are both equal to 1 and each subsequent term is the sum of the two preceding it. The first few terms are <br><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 term are both equal to 1, and each subsequent term is the sum of the two preceding it. The first few terms are <br><math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. |
The Fibonacci sequence can be written [[recursion|recursively]] as <math>F_n=F_{n-1}+F_{n-2}</math>. | The Fibonacci sequence can be written [[recursion|recursively]] as <math>F_n=F_{n-1}+F_{n-2}</math>. | ||
| Line 12: | Line 12: | ||
'''Binet's formula''' is an explicit formula used to find any nth term. | '''Binet's formula''' is an explicit formula used to find any nth term. | ||
| − | It is <math>\frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n\right)</math> | + | It is <math>\frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n\right)</math>. |
{{stub}} | {{stub}} | ||
Revision as of 13:21, 3 July 2006
The Fibonacci sequence is a sequence of integers in which the first and second term 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 
.
Introduction
Ratios between successive terms, 
, 
, 
, 
, 
, tend towards the limit phi.
Intermediate
Binet's formula is an explicit formula used to find any nth term.
It is 
.
This article is a stub. Help us out by expanding it.
