Question

Use the limit comparison test to determine the convergence or divergence of the series.

Answer 1

Step 1:

The series is .

Limit comparison test: Suppose that and are series with positive terms if ,

where is a finite number and , then either both series are convergent or both divergent.

Consider .

Find .

If , then .

From the limit comparison test, both series are convergent or divergent.

Since the harmonic series is convergent, then is also converges by the limit comparison test.

Solution:

The series is is convergent.