Definition:Continued Fraction/Finite

Definition
Let $n \geq 0$ be a natural number.

Informally, a finite continued fraction of length $n$ is an expression of the form:
 * $a_0 + \cfrac 1 {a_1 + \cfrac 1 {a_2 + \cfrac 1 {\ddots \cfrac {} {a_{n-1} + \cfrac 1 {a_n}} }}}$

where $a_0 \in \R$ is any real number and $a_1, a_2, \ldots, a_n$ are any positive real numbers.

Formally, 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 $\left[0 \,.\,.\, n\right]$.

A finite continued fraction should not be confused with its value.

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

Also see

 * Definition:Simple Finite Continued Fraction
 * Definition:Value of Finite Continued Fraction