Ononot — The power series representation of \arctan(x) = \sum{n=0}^{\

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Power Serieshard

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The power series representation of $\arctan(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n+1}$ converges for $x \in [-1, 1]$ . Using Machin's formula $\pi = 12\arctan(1/2) - 4\arctan(1/5)$ and the power series, which truncation gives the best estimate?