What is the Maclaurin series for f(x)=cos2(x)f(x) = \cos^2(x)f(x)=cos2(x)?
1+∑n=1∞(−1)n22n−1x2n(2n)!1 + \sum_{n=1}^{\infty} \frac{(-1)^n 2^{2n-1} x^{2n}}{(2n)!}1+∑n=1∞(2n)!(−1)n22n−1x2n
∑n=0∞(−1)nx2n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}∑n=0∞(2n)!(−1)nx2n
1−∑n=1∞(−1)n22nx2n(2n)!1 - \sum_{n=1}^{\infty} \frac{(-1)^n 2^{2n} x^{2n}}{(2n)!}1−∑n=1∞(2n)!(−1)n22nx2n
12+∑n=1∞(−1)n22n−1x2n(2n)!\frac{1}{2} + \sum_{n=1}^{\infty} \frac{(-1)^n 2^{2n-1} x^{2n}}{(2n)!}21+∑n=1∞(2n)!(−1)n22n−1x2n