Harmonic Series is Divergent/Proof 2

Theorem
The harmonic series:
 * $\displaystyle \sum_{n \mathop = 1}^\infty \frac 1 n$

diverges.

Proof
Observe that all the terms of the harmonic series are strictly positive.

From Reciprocal Sequence is Strictly Decreasing, the terms are decreasing.

Hence the Cauchy Condensation Test can be applied, and we examine the convergence of:

This diverges, from the $n$th term test.

Hence $\displaystyle \sum \frac 1 n$ also diverges.