Question

How to determine whether a series is convergent or divergent? Pleases show your steps?

n=1 to infinity, an= 10/((3n+5)(3n+2))

Answer 1

Step 1 :

If the series is convergent, then we must have .

In particular, if the sequence we are trying to add does not converge to 0, then the associated series is divergent.

Step 2 :

As , then .

Evaluate the limits.

Hence, the series is convergent.

Solution :

The series is convergent.