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Converge or Diverge?

  1. Nov 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Ok, so I was given this problem:

    Ʃ (kth root of k)/k^3 = k^(1/k) / k^3
    k=1

    2. Relevant equations
    None


    3. The attempt at a solution
    I know that I have to use the comparison test, but am unsure how to apply it. Can somebody help me?
     
  2. jcsd
  3. Nov 2, 2012 #2
    You can write that into Ʃk1/k-3. Can you find a nice real number r that has the property that r>1/k-3 for all k and Ʃkr converges?
     
  4. Nov 2, 2012 #3
    No I can't.
     
  5. Nov 2, 2012 #4

    micromass

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    Can you tell us for which real numbers r, the series [itex]\sum_k k^r[/itex] converges?
     
  6. Nov 2, 2012 #5
    I know that the series converges, but do not know what to use for the second series. I need to prove its convergence using one of the tests.
     
  7. Nov 2, 2012 #6

    micromass

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    What series converges?? What second series?? :confused:

    Can you answer my question about [itex]\sum k^r[/itex]?? For which r does it converge?
     
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