Find the Taylor series of f(x)=1x2f(x) = \frac{1}{x^2}f(x)=x21 centered at a=1a = 1a=1.
∑n=0∞(n+1)(x−1)n\sum_{n=0}^{\infty} (n+1)(x-1)^n∑n=0∞(n+1)(x−1)n
∑n=0∞(−1)n(n+1)(x−1)n\sum_{n=0}^{\infty} (-1)^n (n+1)(x-1)^n∑n=0∞(−1)n(n+1)(x−1)n
∑n=0∞(n+1)(x−1)nn!\sum_{n=0}^{\infty} \frac{(n+1)(x-1)^n}{n!}∑n=0∞n!(n+1)(x−1)n
∑n=0∞(−1)n(n+1)(x−1)nn!\sum_{n=0}^{\infty} (-1)^n \frac{(n+1)(x-1)^n}{n!}∑n=0∞(−1)nn!(n+1)(x−1)n