Complete quotient
= Complete quotient
{title2=$\theta_n$}
For a simple <continued fraction>, the complete quotients satisfy $\theta_0=x$, $a_n=\lfloor\theta_n\rfloor$ and $\theta_{n+1}=1/(\theta_n-a_n)$ whenever the denominator is nonzero. Thus $\theta_n=[a_n;a_{n+1},\ldots]$.