Continued Fraction - Basic Formulae

Basic Formulae

A finite continued fraction is an expression of the form

where a0 is an integer, all other ai are positive integers, and n is a non-negative integer.

Thus, all of the following illustrate valid finite continued fractions:

Examples of finite continued fractions
Formula Numeric Remarks
All integers are a degenerate case
Simplest possible fractional form
First integer may be negative
First integer may be zero

An infinite continued fraction can be written as

with the same constraints on the ai as in the finite case.

Read more about this topic:  Continued Fraction

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