Harmonic Series is Divergent/Proof 4

Proof
For all $N \in \N$:


 * $\dfrac 1 N + \dfrac 1 {N + 1} + \cdots + \dfrac 1 {2 N} > N \cdot \dfrac 1 {2 N} = \dfrac 1 2$

Hence, by Cauchy's Convergence Criterion for Series, the Harmonic series is divergent.