What is the Taylor series of f(x)=1xf(x) = \frac{1}{x}f(x)=x1 centered at a=1a=1a=1?
∑n=0∞(x−1)n\sum_{n=0}^{\infty} (x-1)^n∑n=0∞(x−1)n
∑n=0∞(−1)n(x−1)n\sum_{n=0}^{\infty} (-1)^n (x-1)^n∑n=0∞(−1)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∞n(x−1)n\sum_{n=0}^{\infty} n(x-1)^n∑n=0∞n(x−1)n