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

diverges