Find the Taylor series of f(x)=1xf(x) = \frac{1}{x}f(x)=x1 centered at x=1x = 1x=1.
∑n=0∞(−1)n(x−1)n\sum_{n=0}^{\infty} (-1)^n(x-1)^n∑n=0∞(−1)n(x−1)n
1−(x−1)+(x−1)2−(x−1)3+⋯1 - (x-1) + (x-1)^2 - (x-1)^3 + \cdots1−(x−1)+(x−1)2−(x−1)3+⋯
∑n=0∞(1−x)n\sum_{n=0}^{\infty} (1-x)^n∑n=0∞(1−x)n
∑n=1∞(−1)n(x−1)n\sum_{n=1}^{\infty} (-1)^n(x-1)^n∑n=1∞(−1)n(x−1)n