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Theorem: Maclaurin Series of Cosine

For every real number xx,

cos⁡x=∑n=0∞(−1)nx2n(2n)!=1−x22!+x44!−x66!+⋯ ,\cos x = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots,

and the series on the right is the Maclaurin series of cos⁡x\cos x.

27 viewsMathematics · Single Variable Calculus
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