Accuracy of Convergents of Convergent Simple Infinite Continued Fraction

Theorem
Let $C = (a_0, a_1, \ldots)$ be an infinite simple continued fraction in $\R$.

Let $C$ converge to $x \in \R$.

For $n\geq0$, let $p_n/q_n$ be the $n$th convergent of $C$, where $p_n$ and $q_n$ are the $n$th numerator and denominator.

Then for all $n\geq 0$:
 * $\left\vert x - \dfrac {p_n}{q_n}\right\vert < \dfrac 1{q_nq_{n+1}}$.