Find the Taylor series of f(x)=1xf(x) = \frac{1}{x}f(x)=x1 centered at a=1a=1a=1 (first four terms).
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+⋯
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+⋯
x−x2+x3−⋯x - x^2 + x^3 - \cdotsx−x2+x3−⋯
(x−1)−(x−1)2+(x−1)3−⋯(x-1)-(x-1)^2+(x-1)^3-\cdots(x−1)−(x−1)2+(x−1)3−⋯