Find the Maclaurin series for f(x)=sinh(x)=ex−e−x2f(x) = \sinh(x) = \frac{e^x - e^{-x}}{2}f(x)=sinh(x)=2ex−e−x.
∑n=0∞x2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!x2n+1
∑n=0∞x2n(2n)!\sum_{n=0}^{\infty} \frac{x^{2n}}{(2n)!}∑n=0∞(2n)!x2n
∑n=1∞xnn!\sum_{n=1}^{\infty} \frac{x^n}{n!}∑n=1∞n!xn
∑n=0∞(−1)nx2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!(−1)nx2n+1