What is the Maclaurin series for cosh(x)=ex+e−x2\cosh(x) = \displaystyle \frac{e^x + e^{-x}}{2}cosh(x)=2ex+e−x?
∑n=0∞x2n(2n)!\displaystyle \sum_{n=0}^{\infty} \frac{x^{2n}}{(2n)!}n=0∑∞(2n)!x2n
∑n=0∞x2n+1(2n+1)!\displaystyle \sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)!}n=0∑∞(2n+1)!x2n+1
∑n=0∞(−1)nx2n(2n)!\displaystyle \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}n=0∑∞(2n)!(−1)nx2n
∑n=0∞(−1)nxnn!\displaystyle \sum_{n=0}^{\infty} \frac{(-1)^n x^n}{n!}n=0∑∞n!(−1)nxn