Write the Maclaurin series for cosx\cos xcosx and state its radius of convergence.
∑n=0∞(−1)nx2n(2n)!\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n)!}n=0∑∞(2n)!(−1)nx2n, R=∞R=\inftyR=∞
∑n=0∞x2n(2n)!\displaystyle\sum_{n=0}^{\infty}\frac{x^{2n}}{(2n)!}n=0∑∞(2n)!x2n, R=∞R=\inftyR=∞
∑n=0∞(−1)nx2n+1(2n+1)!\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}n=0∑∞(2n+1)!(−1)nx2n+1, R=∞R=\inftyR=∞
∑n=0∞(−1)nx2n(2n)!\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n)!}n=0∑∞(2n)!(−1)nx2n, R=1R=1R=1