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Testing for divergence

  1. Dec 12, 2009 #1
    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?
  2. jcsd
  3. Dec 12, 2009 #2


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  4. Dec 12, 2009 #3
    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..
  5. Dec 12, 2009 #4


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    No, because

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

    so that test doesn't provide any information.
  6. Dec 17, 2009 #5
    oh alright! thank you
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