1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

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

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