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Difference between revisions of "Fibonacci sequence"

(added binet's formula, recursion)
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'''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.
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It is <math>\frac{1}{\sqrt{5}}\left((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)</math>
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It is <math>\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)</math>

Revision as of 16:12, 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 $1,1,2,3,5,8,13,21,34,55,...$. Ratios between successive terms, $\frac{1}{1}$, $\frac{2}{1}$, $\frac{3}{2}$, $\frac{5}{3}$, $\frac{8}{5}$, tend towards the limit phi. The Fibonacci sequence can be written recursively as $F_n=F_{n-1}+F_{n-2}$.

Binet's formula is an explicit formula used to find any nth term. It is $\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)$

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