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Power Seriesmedium
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Using the Taylor series cos⁡(x)=∑n=0∞(−1)nx2n(2n)!\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}cos(x)=∑n=0∞​(2n)!(−1)nx2n​, which is the smallest NNN such that the NNN-th degree Taylor polynomial PN(x)P_N(x)PN​(x) approximates cos⁡(0.2)\cos(0.2)cos(0.2) with error less than 10−510^{-5}10−5?