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WZ
Numerade Educator

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Problem 41 Medium Difficulty

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} $

Answer

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

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Video Transcript

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