**Problem**

The harmonic series is an infinite series given by the sum of reciprocals.

**Part 1:** Use the comparison test to prove that the harmonic series is divergent.

**Part 2:** Use the integral test to prove that the harmonic series is divergent.

**Solution**

**Part 1**
Group the terms in the Harmonic series as follows:

It can be shown that each bracket grouped above is always greater than :

Therefore,

Since

it follows that

- .

**Part 2**

Therefore,

- .

**Historical Note**

This result in Part 1 (using the comparison test) was a proof by the Medieval French theologian, philosopher, and mathematician Nicholas Oresme (c. 1325 - 1382 AD).