1)

Step 1:

The series is .

Test the convergence using ratio test.

Ratio test :

(i) If , then the series is absolutely convergent.

(ii) If or , then the series is divergent.

Step 2:

Here and .

Find

.

Therefore, the series is divergent by the ratio test.

Solution:

The series is  divergent .

f)

Step 1:

The series is .

Test the convergence using ratio test.

Ratio test :

(i) If , then the series is absolutely convergent.

(ii) If or , then the series is divergent.

Step 2:

Here and .

Find

.

Therefore, the series is divergent by the ratio test.

Solution:

The series is  divergent .