OK so i missed this day in class and i've been trying to understand why a harmonic series is divergent. One of our homework problems is this:

We have seen that the harmonic series is a divergent series whose terms approach 0. Show that

Is another series with this property.

With infinite on the top and n=1 on the bottom of the sum sign. I don't know how to do that in LaTex.

My teacher gave use a hint as to how to solve the problem:

The sum separates into

If anyone could show me how to solve this problem, explain harmonic series for me, or direct me to a website that might help i'd really appreciate it. Thanks ^.^