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Calculus II - Infinite Series

  1. Sep 4, 2011 #1
    1. The problem statement, all variables and given/known data

    The sereis sigma[k=1,inf] [(-1)^k/k^p] converges conditionally for
    (a) p<1
    (b) 0<p<=1
    (c) p>1
    (d) p=0
    (e) None of the above

    2. Relevant equations



    3. The attempt at a solution

    The answer key said that (b) was the correct answer and I'm having trouble understanding why

    sigma[k=1,inf] |(-1)^k/k^p| = sigma[k=1,inf] |1/k^p|

    I got rid of the (-1)^k because the absolute value function will always make it positive and k^p will always be positive for k=1 to infinity so I just got ride of the absolute sign all together

    sigma[k=1,inf] 1/k^p

    I thought determine which values of p makes this series converge I could determine what values of the original series allows the series to converge absolutely

    sigma[k=1,inf] 1/k^p

    Is a p-series which converge whenever p is greater one by the integral test

    I don't see were I'm going wrong thanks for any help
     
  2. jcsd
  3. Sep 4, 2011 #2
    You missed the key words, "converges conditionally". When does it converge conditionally? What does that mean?
     
  4. Sep 4, 2011 #3
    ohhhh... that means when you take the absolute function around the function that describes the series what values of p does it diverge in which case it's 0<p<=1, I thought it asked me what values does it converge absolutley by accident thanks
     
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