# Definition:Continued Fraction/Notation

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## Notation for Continued Fraction

A continued fraction can be denoted using ellipsis:

- $a_0 + \cfrac 1 {a_1 + \cfrac 1 {a_2 + \cfrac 1 {\ddots \cfrac {} {} } } }$

Another notation that can sometimes be seen is:

- $a_0 + \dfrac 1 {a_1 +} \dfrac 1 {a_2 +} \dfrac 1 {a_3 + \cdots}$

By definition, a continued fraction is its sequence of partial quotients and can thus be denoted:

- $\sequence {a_n}_{n \mathop \ge 0}$
- $\sqbrk {a_0; a_1, a_2, \ldots}$
- $\sqbrk {a_0, a_1, a_2, \ldots}$

where the last two notations are usually reserved for its value.

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## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**continued fraction**