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 .

.

Therefore, the series converges.

By alternating series test, the series is converges.

-Series test :

If the series where .

If then the series converges.

If  then the series diverges.

Consider the sum of series .

Here .

From the series test, then 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 .

By alternating series the series converges.

The series converges absolutely.