Continued Fraction Expansion of Irrational Square Root/Examples/2

Examples of Continued Fraction Expansion of Irrational Square Root
The continued fraction expansion of the square root of $2$ is given by:
 * $\sqrt 2 = \left[{1, \left \langle{2}\right \rangle}\right]$

Proof
Thus it is possible to replace $\sqrt 2$ recursively:

The pattern repeats indefinitely, producing the continued fraction expansion:
 * $\sqrt 2 = \left[{1, 2, 2, 2, \ldots}\right] = \left[{1, \left \langle{2}\right \rangle}\right]$