Consider the series
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
The series diverges.
Proof. First, we write
We know the series
converges by comparison with . The series
diverges by comparison with . Hence, the difference must diverge (since the sum/difference of a convergent series with a divergent series is divergent)
The first equation in the proof has a typo.