What is the Taylor series of f(x)=exf(x) = e^xf(x)=ex centered at a=0a=0a=0?
∑n=0∞xn\sum_{n=0}^{\infty} x^n∑n=0∞xn
∑n=0∞xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!}∑n=0∞n!xn
∑n=0∞nxnn!\sum_{n=0}^{\infty} \frac{n x^n}{n!}∑n=0∞n!nxn
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn