Which of these series representations is valid 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∞(−1)n+1xnn\sum_{n=1}^{\infty} \frac{(-1)^{n+1} x^n}{n}∑n=1∞n(−1)n+1xn
∑n=0∞(−1)nxnn!\sum_{n=0}^{\infty} \frac{(-1)^n x^n}{n!}∑n=0∞n!(−1)nxn
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn
∑n=0∞x2n+12n+1\sum_{n=0}^{\infty} \frac{x^{2n+1}}{2n+1}∑n=0∞2n+1x2n+1