Given the series $$S = \displaystyle\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}$$, which of the following series has the same convergence behavior as $$S$$?

I. $$\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2n}$$

II. $$\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n + \sin(n)}$$

III. $$\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^{n+1}\sqrt{n}}{n^{3/2}}$$