Discuss the convergence or divergence of the series .
We know the series diverges because it is a p-series with p=1. Since
so, by the direct comparison, our series diverges. We can use the direct comparison test because our series has positive terms and so does the series . Again, this makes sense. If we have a series with positive terms which diverges, then it goes off to infinity. Another series with even bigger positive terms will clearly also go off to infinity.