Thread: Can you use the alternating test to conclude if a series is divergent?

If an infinite series is not monotonically decreasing and if it does not approach 0 but instead approaches infinity, would this be sufficient information to conclude that the series is divergent since it doesn't meet the alternating test's requirements?

Hey MathIsOhSoHard.

Can you outline the example you are talking about?

Originally Posted by chiro

Hey MathIsOhSoHard.

Can you outline the example you are talking about?

Then:


This does not decrease monotonically nor does it approach zero, so would I be able to conclude that it is divergent based on the alternating series test? Or would the test be inconclusive and I'd have to use another test?

The nth term test should show that this diverges as long as n > 4 so you can break up the series with n = 1 to 4 and then another series with n = 4 onwards and show that absolute value is greater than 1 for all terms which means it diverges.