Learning to use "Ratio Test for the convergence" is important. But sometimes you can "eyeball" the answer by looking at the form of the series. I generally enjoy summing up such series. I am sorry for swaying from the main topic, but I want to demonstrate this method. It wont work everywhere but with experience you will know where to use it
The 'n' factor in the denominator looks as though it has been integrated. It is immediate that
for ,
Now substitute and so you even know that