What is the Taylor series for f(x)=exf(x) = e^xf(x)=ex centered at x=1x = 1x=1?
e∑n=0∞(x−1)nn!e \sum_{n=0}^{\infty} \frac{(x-1)^n}{n!}e∑n=0∞n!(x−1)n
∑n=0∞(x−1)nn!\sum_{n=0}^{\infty} \frac{(x-1)^n}{n!}∑n=0∞n!(x−1)n
∑n=0∞xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!}∑n=0∞n!xn
e∑n=1∞(x−1)nne \sum_{n=1}^{\infty} \frac{(x-1)^n}{n}e∑n=1∞n(x−1)n