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Homework Help: Absolute and Conditional Convergence Problem

  1. Dec 6, 2008 #1
    1. The problem statement, all variables and given/known data

    Test the series for (a) absolute convergence, and (b) conditional convergence.

    [tex]\sum\left(-1\right)^{k+1}\frac{k^{k}}{k!}[/tex]

    2. Relevant equations



    3. The attempt at a solution

    So I tried taking the absolute value and then applying the ratio test, which, after simplifying gives me [tex]\frac{\left(k+1\right)^{k}}{k^{k}}[/tex] and then using the root test, but that simplifies to [tex]\frac{k+1}{k}[/tex] which converges at 1 and therefore those tests are inconclusive.
     
  2. jcsd
  3. Dec 6, 2008 #2
    Is k^k > k! true for all k?
     
  4. Dec 6, 2008 #3
    Ahhhhh... divergence test. Wow that was a lot easier than I thought it was. So the term goes to infinity and the series diverges. Thank you so much for your help!
     
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