Find the Taylor series for f(x)=ln(x)f(x) = \ln(x)f(x)=ln(x) centered at a=2a=2a=2.
ln(2)+∑n=1∞(−1)n−1n2n(x−2)n\ln(2) + \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n 2^n} (x-2)^nln(2)+∑n=1∞n2n(−1)n−1(x−2)n
ln(2)+∑n=1∞(−1)n−1n(x−2)n\ln(2) + \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} (x-2)^nln(2)+∑n=1∞n(−1)n−1(x−2)n
ln(2)+∑n=1∞1n2n(x−2)n\ln(2) + \sum_{n=1}^{\infty} \frac{1}{n 2^n} (x-2)^nln(2)+∑n=1∞n2n1(x−2)n
∑n=0∞(−1)nn!(x−2)n\sum_{n=0}^{\infty} \frac{(-1)^n}{n!} (x-2)^n∑n=0∞n!(−1)n(x−2)n