The series is .

Check for the convergence of the alternate series test.

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 monotonic decreasing from .

.

.

Here because .

Thus, series is convergent by alternating series test.

Definitions of Absolute and conditional convergence :

(1) is Absolutely convergent if converges.

(2) is Conditionally convergent if converges but diverges.

Check the  absolutely convergence of .

Find convergence of .

term test for convergent series :

If converges then .

is convergent series.

Thus, From the definition is  converges absolutely.

is  converges absolutely.