Definition:Convergent of Continued Fraction/Even

Definition
Let $C = \left[{a_1, a_2, a_3, \ldots, a_n}\right]$ or $\left[{a_1, a_2, a_3, \ldots}\right]$ be a continued fraction, either finite or infinite.

Let the $k$th convergent $C_k$ of $C$ be the finite continued fraction:
 * $C_k = \left[{a_1, a_2, \ldots, a_k}\right]$

The even convergents of $\left[{a_1, a_2, a_3, \ldots, a_n}\right]$ are the convergents $C_2, C_4, C_6, \ldots$, that is, those with an even subscript.