Consider the series
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
The given series converges conditionally.
Proof. First, we have
Furthermore, the sequence of terms is monotonically decreasing. We can see this by looking at
This derivative is negative for all (since the numerator is negative and the denominator is always positive). Hence, the sequence is monotonically decreasing. Therefore, by the Leibniz rule we have
This convergence is conditional since
This series diverges by the comparison test since