The series is .

Divergence test:

For the series , If , then the series is divergent and \ \

If , then the series is convergent.

Here .

Find out the first few terms.

If then .

If then .

If then .

Observe the terms:

The common ratio is .

.

Since the series is geometric and , the series converges.

Therefore the sum of the series is calculated by using the formula .

.

Therefore the series is convergent and sum of the series is .

The series is convergent and sum of the series is .