series?

Question

Answer 1

(a)

Step 1:

The series is .

Use the ratio test to determine series is absolutely convergent, conditionally convergent or divergent.

Ratio Test :

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

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

(iii) If , then the ratio test is inconclusive.

Step 2:

The series is .

Consider .

Apply ratio test :

Since , the series is divergent.

Solution :

The series is divergent.

Answer 2

(b)

Step 1:

The series is .

Use the ratio test to determine series is absolutely convergent, conditionally convergent or divergent.

Ratio Test :

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

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

(iii) If , then the ratio test is inconclusive.

Step 2:

The series is .

Consider .

Apply ratio test :

Since the series is divergent.

Solution :

The series is divergent.