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Does the Series Converge or Diverge?

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine whether the infinite series converges or divergens. If it converges find its sum.
    [itex] \sum^{∞}_{k=1} \frac{k-3}{k}[/itex]


    2. Relevant equations



    3. The attempt at a solution

    I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.


    However, I'm not sure if I'm using the test for divergence right.
     
  2. jcsd
  3. Apr 29, 2012 #2


    You are contradicting yourself. Do you think it converges or diverges ?

    Hint: This series doesn't converge try and use a comparison test too see why.
     
  4. Apr 29, 2012 #3
    Sorry, I ment to say that the series diverges by the test for divergence because the limit is not equal to 0.
     
  5. Apr 29, 2012 #4
    Yes, by the non null test is this is divergent as the limit is not equal to zero.
     
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