Testing for divergence

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

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Yes.
 
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

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No, because

[tex]
\lim_{n \to \infty} \frac{(-1)^n}{n} = 0
[/tex]

so that test doesn't provide any information.
 
oh alright! thank you
 

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