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Using ratio test to test conditional convergence?

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data
    So what I was taught was that if the lim of the ratio test is the series is always absolutely convergent. If it is >1 the series is always divergent. But if it is =1 then we don't know. So would that mean that all conditionally convergent series would have a limit = 1? I am confused :s

    Thanks!
     
  2. jcsd
  3. Mar 25, 2012 #2

    Dick

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    Yes, if the ratio test applied to conditional convergent series exists, then it must be 1. On the other hand, the ratio test might not give you a limit at all. In that case the series can do anything it wants to.
     
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