## Calculus (3rd Edition)

$$\Sigma_{n=0}^\infty \frac{1}{n}$$
The easiest example is the P-series: $$\Sigma_{n=0}^\infty \frac{1}{n}$$ it is divergent since $p=1$ (harmonic series). At the same time, we have $\lim_{n\to \infty}\frac{1}{n}=0.$