Find the Taylor series of f(x)=e2xf(x) = e^{2x}f(x)=e2x centered at a=0a = 0a=0.
∑n=0∞xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!}∑n=0∞n!xn
∑n=0∞2nxnn!\sum_{n=0}^{\infty} \frac{2^n x^n}{n!}∑n=0∞n!2nxn
∑n=0∞2xnn!\sum_{n=0}^{\infty} \frac{2x^n}{n!}∑n=0∞n!2xn
∑n=0∞x2nn!\sum_{n=0}^{\infty} \frac{x^{2n}}{n!}∑n=0∞n!x2n