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Use the power series for $ tan^{-1} x $ to prove the following expression for $ \pi $ as the sum of an infinite series:

$ \pi = 2 \sqrt 3 \sum_{n = 0}^{\infty} \frac {(-1)^n}{(2n + 1) 3^n} $

$$2 \sqrt{3} \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1) 3^{n}}$$

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Campbell University

Harvey Mudd College

Baylor University

Boston College

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