Identify the Maclaurin series for f(x)=ln(1−x)f(x) = \ln(1-x)f(x)=ln(1−x) for ∣x∣<1|x|<1∣x∣<1.
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn
−∑n=1∞xnn-\sum_{n=1}^{\infty} \frac{x^n}{n}−∑n=1∞nxn
∑n=0∞(−1)nxn\sum_{n=0}^{\infty} (-1)^n x^n∑n=0∞(−1)nxn
∑n=1∞(−1)nxnn\sum_{n=1}^{\infty} \frac{(-1)^n x^n}{n}∑n=1∞n(−1)nxn