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pastmarion
pastmarion
15.04.2020 • 
Mathematics

(5 pts) If one wants to calculate π to an arbitrary number of decimal places, the best way to do this is to use a power series representation. In this problem we will derive a formula for this. (a) Find a power series representation of the function f(x) = tan−1 x. You can do this by noticing that tan−1 x = Z 1 1 + x 2 dx and integrating the power series representation of the right hand side term-byterm. Be sure to find the value of C. (b) Use the previous step to derive that π = 2√ 3 X[infinity] n

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