Find the Taylor series of f(x)=ln(x)f(x) = \ln(x)f(x)=ln(x) centered at x=1x = 1x=1.
∑n=1∞(−1)n−1n(x−1)n\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n}(x-1)^n∑n=1∞n(−1)n−1(x−1)n
∑n=1∞(−1)nn(x−1)n\sum_{n=1}^{\infty} \frac{(-1)^{n}}{n}(x-1)^n∑n=1∞n(−1)n(x−1)n
∑n=0∞(−1)nn+1(x−1)n+1\sum_{n=0}^{\infty} \frac{(-1)^{n}}{n+1}(x-1)^{n+1}∑n=0∞n+1(−1)n(x−1)n+1
∑n=1∞(x−1)nn2\sum_{n=1}^{\infty} \frac{(x-1)^n}{n^2}∑n=1∞n2(x−1)n