The series is .

Alternate series test :

Let ,The alternate series test and converge if it satisfies the following conditions.

(1). ,

(2). for all values of .

.

is positive and decreasing from .

.

Apply the formula :.

Therefore, the series converges.

Definitions of Absolute and conditional convergence :

(1) is Absolutely convergent if converges.

(2) is Conditionally convergent if converges but diverges.

Check the convergence of .

The series diverges.

does not convergent absolutely.

From the definitions series converges conditionally.

The series converges conditionally.