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Stephenson:Neal:Quicksilver:316:the first few terms of a series (jere7my tho?rpe)

From the Quicksilver Metaweb.

We have now seen two generations of the Waterhouse family educated in the Leibniz series. The mathematical series that Leibniz sketches in the dirt for Daniel Waterhouse:

\frac{\pi}{4}=\frac{1}{1}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}\cdots

is shown by Alan Turing to Lawrence Waterhouse on page 15 of Cryptonomicon, in a more compact (and modern) form:

\pi = 4\sum_{n=0}^\infty \frac{(-1)^n}{2n+1}