Find the Taylor series for f(x)=ln(x)f(x) = \ln(x)f(x)=ln(x) centered at x=1x = 1x=1 (first 3 terms).
(x−1)−(x−1)22+(x−1)33+⋯(x-1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} + \cdots(x−1)−2(x−1)2+3(x−1)3+⋯
1+(x−1)−(x−1)22+⋯1 + (x-1) - \frac{(x-1)^2}{2} + \cdots1+(x−1)−2(x−1)2+⋯
(x−1)−(x−1)22!+(x−1)33!+⋯(x-1) - \frac{(x-1)^2}{2!} + \frac{(x-1)^3}{3!} + \cdots(x−1)−2!(x−1)2+3!(x−1)3+⋯
ln(1)+x−11−(x−1)24+⋯\ln(1) + \frac{x-1}{1} - \frac{(x-1)^2}{4} + \cdotsln(1)+1x−1−4(x−1)2+⋯