Consider the series
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
If then the series diverges since
as
.
If then the series converges by the Leibniz rule since
is decreasing and
.
The convergence is absolute if and only if since
converges if and only if (by the integral test, Example #1 on page 398 of Apostol).