You can put this solution on YOUR website! It is quite difficult to come up with an explicit formula for the nth partial sum of the harmonic series, but there is a famous theorem which says that
This essentially says that the difference between the nth partial sum and ln n approaches a constant (known as the Euler-Mascheroni constant) as n gets really large.
Obviously, the infinite sum
diverges due to the integral test. Since
the integral diverges and so does the infinite sum.
Here is some more information on the nth partial sums of the harmonic series:
http://en.wikipedia.org/wiki/Harmonic_number
