Hi in my book there is a series:

$$\sum\_{n=1}^{\infty} (-1)^n \cdot \frac{1}{n}$$ 

the context is convergence and so on. And this series serves as an exampel for a not absolut convergent but convergent series. For me it looks like the harmonic series, which clearly diverges:

$$\sum\_{n=1}^{\infty} \frac{(-1)^n}{n}$$=$$\sum\_{n=1}^{\infty} |\frac{1}{n}|$$

Am I wrong?