The Fibonacci Series

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The Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci (fi-bo-na-chee) in 1202. It is a deceptively simple series, but its ramifications and applications are nearly limitless. It has fascinated and perplexed mathematicians for over 700 years, and nearly everyone who has worked with it has added a new piece to the Fibonacci puzzle, a new tidbit of information about the series and how it works. Fibonacci mathematics is a constantly expanding branch of number theory, with more and more people being drawn into the complex subtleties of Fibonacci's legacy. 

  

Fibonacci series definition

Fi·bo·nacci series (fē′bə nä′c'hē)

a sequence of integers in which each integer (Fibonacci number) after the second is the sum of the two preceding integers; specif., the series 1, 1, 2, 3, 5, 8, 13, . . .

The Fibonacci numbers are the sequence of numbers defined by the linear recurrence equation,

 

(1)

with .

As a result of the definition (1), it is conventional to define .

The Fibonacci numbers for , 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ...