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