The series is.

Where is a sequence of posittive terms and converges to .

Find the convergence of the series by Root test.

Here .

As the cosine is an alternating series for all integrer values of .

.

Root test :

Let be a series.

1. converges absolutely if .

2. diverges if or .

3. The root test is inconclusive if .

Find .

.

Therefore, the series is absolutely convergent by Root test.

The series is absolutely convergent.