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

1. ## Can you use the alternating series 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?

2. ## Re: Can you use the alternating test to conclude if a series is divergent?

Hey MathIsOhSoHard.

Can you outline the example you are talking about?

3. ## Re: Can you use the alternating test to conclude if a series is divergent?

Originally Posted by chiro
Hey MathIsOhSoHard.

Can you outline the example you are talking about?
$\sum^\infty_{n=1}(-2)^n\frac{1}{n^2+7}$

Then:
$a_n=\frac{2^n}{n^2+7}$

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?

4. ## Re: Can you use the alternating test to conclude if a series is divergent?

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.