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== III. Computer Programming == | == III. Computer Programming == | ||
− | Computers are good at computing! We have seen | + | Computers are good at computing! We have seen various definitions of Euler's number $e$, of which, in particular: |
$$\label{eq:e1}e=\lim_{n\rightarrow\infty}\left(1+{1\over n}\right)^n$$ | $$\label{eq:e1}e=\lim_{n\rightarrow\infty}\left(1+{1\over n}\right)^n$$ | ||
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+ | $$\label{eq:e2}e=\sum_{k=0}^\infty{1\over k !}$$ | ||
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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. | ||
{{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.