Find the Taylor series of f(x)=exf(x) = e^xf(x)=ex centered at a=1a=1a=1.
∑n=0∞en!(x−1)n\sum_{n=0}^{\infty} \frac{e}{n!} (x-1)^n∑n=0∞n!e(x−1)n
∑n=0∞1n!(x−1)n\sum_{n=0}^{\infty} \frac{1}{n!} (x-1)^n∑n=0∞n!1(x−1)n
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∞en(x−1)n\sum_{n=0}^{\infty} e^n (x-1)^n∑n=0∞en(x−1)n