Difference between revisions of "Fibonacci sequence"
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| − | The '''Fibonacci sequence''' is a series of numbers in which each number is the sum of the two preceding it (the first two terms are simply 1). The first few terms are <math>1,1,2,3,5,8,13,21,34,55,...</math>. | + | The '''Fibonacci sequence''' is a series of numbers in which each number is the sum of the two preceding it (the first two terms are simply 1). The first few terms are <br><math>1,1,2,3,5,8,13,21,34,55,...</math>. |
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The Fibonacci sequence can be written recursively as <math>F_n=F_{n-1}+F_{n-2}</math>. | The Fibonacci sequence can be written recursively as <math>F_n=F_{n-1}+F_{n-2}</math>. | ||
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| + | == Introduction == | ||
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| + | Ratios between successive terms, <math>\frac{1}{1}</math>, <math>\frac{2}{1}</math>, <math>\frac{3}{2}</math>, <math>\frac{5}{3}</math>, <math>\frac{8}{5}</math>, tend towards the limit [[phi]]. | ||
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| + | == Intermediate == | ||
'''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}}((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)</math> | It is <math>\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)</math> | ||
Revision as of 16:31, 20 June 2006
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding it (the first two terms are simply 1). 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 
