Continued Fraction Identities/First/Infinite

Theorem
Let $\left[{a_1, a_2, a_3, \ldots}\right]$ be the continued fraction expansion of a simple infinite continued fraction.

Then:


 * $\left[{a_1, a_2, a_3, \ldots}\right] = a_1 + \dfrac 1 {\left[{a_2, a_3, \ldots}\right]}$

Proof
This follows directly from the definition of a simple infinite continued fraction and continued fraction expansion.