Here’s another example of a mathematical identity that is almost magical:

$$ \frac {\pi} {4} = 1 – \frac{1}{3} + \frac{1}{5} – \frac{1}{7} +…$$

The beauty lies in the apparent simplicity of this, along with the fundamental question of why the interminable expression on the right results in increasingly better approximations to $ \pi$.

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