Definition:Convergent of Continued Fraction/Definition 2

Definition
The $k$th convergent $C_k$ of $C$ is the quotient of the $k$th numerator $p_k$ by the $k$th denominator $q_k$:
 * $C_k = \dfrac {p_k} {q_k}$

Also see

 * Equivalence of Definitions of Convergent of Continued Fraction