Definition

Approximation as infinite series

Approximation as infinite continued fraction

Or, writing it in one line become

Very condense form of continued fraction is show that the continued fraction of has regular pattern of where is increasing even numbers.

MS excel function of Euler number is =EXP(1)

Now you can download the Spreadsheet companion of this tutorial and try PI() for different accuracy

For example:

Accuracy |
Exp as ratio |
Error (computed from PI of MS Excel) |

0.1 |
||

0.001 |
||

0.00001 |
||

0.0000001 |

**Preferable reference for this tutorial is**

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