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Convergence or Divergence of a series

  1. Feb 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Does sum from n=1 to n=infinity of 1/[n^(1+1/n)]
    converge or diverge.

    2. Relevant equations

    ^^^^^^^^^^^^^^^

    3. The attempt at a solution
    The general term goes to 0 and its a p-series with p>1, but for large n the series becomes 1/n pretty much so, even tho p>1 is it divergent?
     
  2. jcsd
  3. Feb 27, 2015 #2

    LCKurtz

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    It isn't a ##p## series but, as you say, it's "like" a ##p## series with ##p=1## as ##n## gets large. So if I were you, I would try a limit comparison test with ##\sum\frac 1 n## and see.
     
    Last edited: Feb 27, 2015
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