Continued Fraction Identities/First/Infinite

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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


$\blacksquare$