Definition:Convergent of Continued Fraction/Definition 2
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Definition
Let $F$ be a field, such as the field of real numbers.
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 $n$.
Let $k \le n$ be a natural number.
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
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continued fraction