Consider the series
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
The given series is conditionally convergent.
Proof. By the Leibniz rule we know that if is a monotonic decreasing sequence with , then the alternating series converges. In this case we have
is monotonic decreasing with . Hence, the alternating series
converges. This convergence is conditional since