1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook