I Know that $\sum_{n=1}^\infty \frac{1}{n}$ Diverges, but what is $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}$
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $