# Definition:Convergent of Continued Fraction/Even

## Definition

Let $F$ be a field.

Let $n \in \N \cup \set \infty$ be an extended natural number.

Let $C = \sqbrk {a_0, a_1, a_2, \ldots}$ be a continued fraction in $F$ of length $n$.

The even convergents of $\sqbrk {a_0, a_1, a_2, \ldots}$ are the convergents $C_0, C_2, C_4, \ldots$, that is, those with an even subscript.