Direct comparison test :

Let  for all .

1.If  convergence, then  convergence.

2.If  diverges, then  diverges.

The series is .

Here  and .

Observe that .

The series is in the form of geometric series.

The general form of geometric series is .

Here  and .

 is geometric series.

Convergence of a geometric series :

A geometric series with common ratio  diverges if .

If  then the series converges to the sum .

 with ratio .

The series is converges to the sum of series.

.

The series is converges to .

Using the direct comparision test if the series  is converges, then  is converges.

Therefore, the series  is converges.

The series  is converges.