Definition:Continued Fraction/Infinite

Definition
Let $a_1 \in \R$ be any real number and $a_2, a_3, \ldots, a_n, \ldots$ be any infinite sequence in $\R_{\ne 0}$.

Then the expression:


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

is an infinite continued fraction.

An infinite continued fraction is often abbreviated ICF.