Testing Divergence: Alternating Series

[Sahara]

Can the Test for Divergence (limit of an->infinity not equal to zero) be used on an alternating series?
For example, if a series has a (-1)^n term. Can we assume that since the limit of that term does not exist, then the series is automatically diverging?

 

[arildno]

Yes.

 

[Sahara]

Ok,
but what about the sum of ((-1)^n)/n? Doesn't the divergence test say that this sum diverges because of the alternating 1, while the series converges with the alternating series test..

 

[statdad]

No, because

$$\lim_{n \to \infty} \frac{(-1)^n}{n} = 0$$

so that test doesn't provide any information.

 

[Sahara]

oh alright! thank you