## What is Continued Fraction?

Continued fraction is nested fraction or a sequence of fraction. The following expression is called
*
continued fraction
*

It forms two series of numbers
and
. If the sequence
all become 1, we have what is called
**
Regular Continued Fraction
**
, written as

The number
is called the
*
approximant
*
or
*
*
the
*
convergence
*
of continued fraction. The variables in the series
are natural numbers, which sometimes called
*
element
*
or
*
term
*
. For infinite continued fraction, the approximant will converge to a limit convergence value
. Note however that convergence to infinity
is also acceptable.

To save space, we usually use the following line notation to express continued fraction

The condense notation of regular continued fraction is . Personally, I prefer this condense notation as long as it is clear that nominator is always one (i.e. regular continued fraction). When we use a continued fraction but the nominators are not necessarily one (i.e. non-regular continued fraction), in this case, we should use line notation as the most condense notation.

In this tutorial, we will focus only to regular continued fraction, which have 1 as nominators.

## Example

: (how to read the condense notation),

,

This tutorial is copyrighted .

**
Preferable reference for this tutorial is
**

Teknomo, Kardi (2015) Continued Fraction. http://people.revoledu.com/kardi/tutorial/ContinuedFraction/index.html