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Convergence? (analysis)

  1. Sep 21, 2007 #1
    [tex]\sum_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}\][/tex]

    Does this series converge?
     
  2. jcsd
  3. Sep 21, 2007 #2

    Gib Z

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    Homework Helper

    No it doesn't, because [tex]\sqrt[n]{n}}[/tex] approaches 1 as n approaches infinity. Hence if we were to the the first k partial sums of the series in your post, and the harmonic series, the difference would approach a constant as k approached infinity. Since the harmonic series diverges, so does this one.
     
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