Consider the series

Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.

The given series is absolutely convergent.

*Proof.* We can see this since

This series converges by the integral test (example #2 on page 398 of Apostol)

“This series converges by the integral test (example #2 on page 398 of Apostol)” That example is different but you can prove it by comparison.