Question

Use the root test to determine the convergence or divergence of the series.

Answer 1

Step 1:

The series is .

Root test :

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

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

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

Step 2:

Here  and .

Find .

Hence, by the root test, the series is convergent.

Solution:

The series is convergent.