What is the Taylor series of f(x)=lnxf(x) = \ln xf(x)=lnx centered at a=1a=1a=1?
∑n=1∞(−1)n−1(x−1)nn\sum_{n=1}^{\infty} (-1)^{n-1} \frac{(x-1)^n}{n}∑n=1∞(−1)n−1n(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)nn\sum_{n=1}^{\infty} (-1)^n \frac{(x-1)^n}{n}∑n=1∞(−1)nn(x−1)n
∑n=0∞(−1)n(x−1)nn!\sum_{n=0}^{\infty} (-1)^n \frac{(x-1)^n}{n!}∑n=0∞(−1)nn!(x−1)n