Question

Answer 1

e)

Step 1:

The series is .

Test the convergence using ratio test.

The Ratio Test:

Let  be a series with nonzero terms.

1) converges absolutely if .

2) diverges if and .

3) The Ratio Test is inconclusive if .

Step 2:

Here and .

Find .

.

Therefore, by the ratio test the series is divergent .

Solution:

The series is  divergent.

Answer 2

f)

Step 1:

The series is .

Test the convergence using ratio test.

The Ratio Test:

Let  be a series with nonzero terms.

1) converges absolutely if .

2) diverges if and .

3) The Ratio Test is inconclusive if .

Step 2:

Here and .

Find .

.

Therefore, the series is divergent by the ratio test.

Solution:

The series is  divergent .