# Continued Fraction Identities/First/Infinite

## Theorem

Let $\left[{a_0, a_1, a_2, \ldots}\right]$ be 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

$\blacksquare$