Which is the Maclaurin series for ln(1+x)\ln(1+x)ln(1+x) valid for ∣x∣≤1|x| \leq 1∣x∣≤1 (except at x=−1x = -1x=−1)?
∑n=1∞(−1)n+1xnn\sum_{n=1}^{\infty} \frac{(-1)^{n+1} x^n}{n}∑n=1∞n(−1)n+1xn
∑n=0∞(−1)nxn\sum_{n=0}^{\infty} (-1)^n x^n∑n=0∞(−1)nxn
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn
∑n=1∞(−1)nxnn\sum_{n=1}^{\infty} \frac{(-1)^n x^n}{n}∑n=1∞n(−1)nxn