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

Question

Confirm that the integral test can be applied to the series. Then use the integral test to determine the convergence or divergence of the series.

Answer 1

Step 1:

The series is .

Rewrite the series as .

The summation notation of series is .

Let the function be .

The function is continuous and positive for all values of .

Find the derivative of the function.

Apply quotient rule in derivatives .

the function is decreasing for .

is positive, continuous and decreasing for .

is satisfies the conditions of Integral Test.

Integral Test is applicable for the series series.

Step 2:

Apply formula .

In this case .

The series is converges.

Solution:

The series is converges.