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# Convergents

 Convergents[list] gives a list of the convergents corresponding to the continued fraction terms list. Convergents gives the first n convergents for a number x. Convergents[x]gives if possible all convergents leading to the number x.
• The convergents of the continued fraction are the rationals .
• For exact numbers, Convergents[x] can be used if x is rational or a quadratic irrational.
• If x is a quadratic irrational or a representation of a quadratic irrational as a continued fraction, the final list element returned by Convergents[x] is the quadratic irrational represented by x.
• For inexact numbers, Convergents[x] generates a list of all convergents that can be obtained given the precision of x.
• Convergents will return n convergents if possible. If x represents a rational or an inexact number, fewer than n terms may be returned.
Generate the first 10 convergents to the golden ratio:
Generate convergents from the continued fraction terms for GoldenRatio:
Generate the first 10 convergents to the golden ratio:
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Generate convergents from the continued fraction terms for GoldenRatio:
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 Scope   (4)
Quadratic irrationals have periodic continued fractions:
Give all convergents for a rational number:
Convergents continues until the precision of the input is reached:
The convergents of a number converge to it while alternating sides:
The results from Rationalize are not always among the list of convergents:
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