2.18 Euler’s number e

Recall ‘$n$ factorial’ $n!=n(n-1)(n-2)\dots 3.2.1$, which grows very rapidly when the integer $n$ becomes large. Hence the series

converges to the number that we call $e$ is memory of Euler; $e$ is also called the base of natural logarithms.

Calculation of $e$. The first row gives the summands, while the next row gives the decimal approximation, as obtained by repeatedly dividing.