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Continued fraction is a very useful tool of analysis. Many iterations-algorithms can be expressed easily using continued fraction. Continued fraction has nice property that it converge very fast (some are better than power series) and it can be useful to approximate the real number as ratio of two integers. This tutorial is an introduction to regular continued fraction (finite, infinite and periodic) and its application to convert decimal to fraction, compute Pi and Euler number. MS Excel spreadsheet companion of this tutorial can be downloaded for free
What is Continued Fraction?
Why and when do we use Continued Fraction?
How do we compute Continued Fraction?
Relationship of Continued Fraction and Difference Equation
Periodic Continued Fraction
Properties of Continued Fraction
Continued Fraction Using Mathematica
See also: Difference Equation tutorial
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Preferable reference for this tutorial is
Teknomo, Kardi (2015) Continued Fraction. http://people.revoledu.com/kardi/tutorial/ContinuedFraction/index.html