Definition:Continued Fraction/Simple/Finite

Definition
Let $a_1, a_2, a_3, \ldots, a_n \in \Z_{>0}$ be strictly positive integers.

Then 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 simple finite continued fraction.

That is, a simple finite continued fraction is a finite continued fraction whose partial quotients are all strictly positive integers.

A simple finite continued fraction can be abbreviated SFCF.

Also known as
A simple finite continued fraction is also known as a regular finite continued fraction.