Use the known Maclaurin 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 to find ∑n=0∞(−1)n22n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^n 2^{2n}}{(2n)!}∑n=0∞(2n)!(−1)n22n.
cos(2)\cos(2)cos(2)
cos(1)\cos(1)cos(1)
1cos(2)\frac{1}{\cos(2)}cos(2)1
cos(2)2\frac{\cos(2)}{2}2cos(2)