Given f(x)=∑n=0∞xnn!f(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}f(x)=∑n=0∞n!xn, what is the Maclaurin series for g(x)=f(2x)g(x) = f(2x)g(x)=f(2x)?
∑xnn!\sum \frac{x^n}{n!}∑n!xn
∑2nxnn!\sum \frac{2^n x^n}{n!}∑n!2nxn
∑xn2nn!\sum \frac{x^n}{2^n n!}∑2nn!xn
∑2xnn!\sum \frac{2 x^n}{n!}∑n!2xn