$\ln(x) = \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}(x-1)^n$ with interval $0 < x \le 2$

$\ln(x) = \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}(x-1)^n$ with interval $0 < x < 2$

$\ln(x) = (x-1) + \sum_{n=2}^{\infty} \frac{(-1)^{n+1}}{n}(x-1)^n$ with $R = 2$

$\ln(x) = \sum_{n=0}^{\infty} \frac{(-1)^{n}}{n+1}(x-1)^{n+1}$ with interval $0 < x \le 2$