(a)

and are series with positive terms.

Suppose that and diverges.

From the definition of limit of convergence there exist such that for all ,.

Which means .

If diverges then so does .

Hence by the comparision test is diverges.

(b)

(i) The series is .

Consider .

Let and it is diverges by -series test.

Find .

.

If and diverges then the series is diverges.

The series is diverges.

(ii) The series is .

Let and diverges.

Find .

.

If and diverges then the series is diverges.

The series diverges.

(a) If and diverges then the series is diverges.

(b)

(i) The series is diverges.

(ii) The series diverges.