1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?