Definition:Continued Fraction/Finite

Informal definition
Let $a_1 \in \R$ be any real number and $a_2, a_3, \ldots, a_n$ be any positive real numbers.

Informally, the expression:


 * $a_1 + \cfrac 1 {a_2 + \cfrac 1 {a_3 + \cfrac 1 {\ddots \cfrac {} {a_{n-1} + \cfrac 1 {a_n}} }}}$

is a finite continued fraction.

Definition
Let $n \geq1$ be a natural number.

A finite continued fraction of length $n$ in $\R$ is a finite real sequence, called sequence of partial quotients, whose domain is the integer interval $\left[0 \,.\,.\, n\right]$

Also known as
A finite continued fraction is often abbreviated FCF, and is also known as a terminated continued fraction.

Also see

 * Definition:Value of Finite Continued Fraction