Determine the power series of f(x)=sinh(x)f(x) = \sinh(x)f(x)=sinh(x) centered at x=0x=0x=0.
∑n=0∞x2n(2n)!\sum_{n=0}^{\infty} \frac{x^{2n}}{(2n)!}∑n=0∞(2n)!x2n
∑n=0∞x2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!x2n+1
∑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
∑n=0∞xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!}∑n=0∞n!xn