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A computer would make a great job of checking this, in particular when convergence is slow. It will also allow us to deepen this important business of convergence. | A computer would make a great job of checking this, in particular when convergence is slow. It will also allow us to deepen this important business of convergence. | ||
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| + | Let us compute \ref{eq:1} | ||
{{WLP6}} | {{WLP6}} | ||
Computers are good at computing! We have seen various definitions of Euler's number $e$, of which, in particular:
$$\tag{1}e=\lim_{n\rightarrow\infty}\left(1+{1\over n}\right)^n$$
$$\tag{2}e=\sum_{k=0}^\infty{1\over k !}$$
A computer would make a great job of checking this, in particular when convergence is slow. It will also allow us to deepen this important business of convergence.
Let us compute \ref{eq:1}