Simple continued fraction

Definition

A simple continued fraction is a continued fraction whose partial numerators are all $1$ . Its first term $a_0$ is an integer, and its later terms $a_1, a_2, \dots$ are positive integers: $[a_0; a_1, a_2, \dots] = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cdots}}$ The sequence of terms can be finite or infinite.

Remarks

The $a_n$ are called the partial quotients. For example, $[2; 3, 4] = 2 + \frac{1}{3 + 1/4} = \frac{30}{13}$ . An infinite simple continued fraction always converges, by the convergence of the convergents. Each real number has a continued fraction expansion of this form.

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Continued fraction definition
Simple continued fraction definition

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Tag	`06XF7BCFFJ`
URI	`m2://06XF7BCFFJ`
Aliases	`regular-continued-fraction`
Kind	definition
Writing	W1 stated
MSC	11A55
Defines	Simple continued fraction
Uses	Continued fraction

Simple continued fraction

Definition

Remarks

Reading path

Where this leads

Further reading

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