The Definition of e
by Mike Martin

This page allows you to investigate the definition of an irrational number, e. The defining formula for e is:

To investigate this we consider the sequence whose nth term is given by

The sequence approaches a limit, e, as the term number grows without bound and after N terms the sequence value is within ε units of that limiting value. This tool is designed for you to investigate the relationship between N and ε, placing it in some context with the definition of the limit of a sequence. The irrational number e is, to 16 decimal places, approximately equal to 2.7182818284590452.

Enter the value of the parameters below, then press Evaluate.

ε =

ymin =

ymax =

nmin =

nmax =