Question
Apply the divergence test to the following and then select the answer choice that best fits the result.
Select the correct answer below:
The divergence test is inconclusive.
The series diverges.

The divergence test states that if the limit of the terms of a series does not approach zero as the number of terms goes to infinity, then the series diverges. In simpler terms, if you’re adding up a bunch of numbers that don’t vanish, you can be sure you’re headed for infinity (divergence)!

However, if the limit of the terms is zero, that doesn’t guarantee convergence; it just means you might have a chance for a neatly behaved series. So if you found that the individual terms don’t disappear as you add more of them, you can feel confident about declaring a clear divergence!