Fibonacci sequence

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
$1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...$ .

The Fibonacci sequence can be written recursively as $F_n=F_{n-1}+F_{n-2}$ .

Introduction

Ratios between successive terms, $\frac{1}{1}$ , $\frac{2}{1}$ , $\frac{3}{2}$ , $\frac{5}{3}$ , $\frac{8}{5}$ , tend towards the limit phi.

Intermediate

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

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Fibonacci sequence

Introduction

Intermediate

See also