Determine the Taylor series for f(x)=ln(x)f(x) = \ln(x)f(x)=ln(x) centered at a=1a=1a=1.
∑n=1∞(−1)n−1(x−1)nn\sum_{n=1}^{\infty} \frac{(-1)^{n-1} (x-1)^n}{n}∑n=1∞n(−1)n−1(x−1)n
∑n=0∞(−1)n(x−1)nn!\sum_{n=0}^{\infty} \frac{(-1)^n (x-1)^n}{n!}∑n=0∞n!(−1)n(x−1)n
∑n=1∞(x−1)nn\sum_{n=1}^{\infty} \frac{(x-1)^n}{n}∑n=1∞n(x−1)n
∑n=1∞(−1)n(x−1)n\sum_{n=1}^{\infty} (-1)^n (x-1)^n∑n=1∞(−1)n(x−1)n