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Series Convergence

  1. Apr 17, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove that the series [itex]\sum_{n=1}^{\infty}\frac{\sqrt{n+1}-\sqrt{n}}{n}[/itex] converges.


    3. The attempt at a solution
    I think I'm going to use the comparison test but I'm having trouble coming up with a series to compare it to. Any clues would be great. Thanks!
     
  2. jcsd
  3. Apr 17, 2014 #2

    SammyS

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    Try rationalizing the numerator.
     
  4. Apr 17, 2014 #3
    Yeah, I've gotten to that point, so as of now I have: [itex]\sum_{n=1}^{\infty}\frac{1}{n(\sqrt{n+1}+\sqrt{n})}[/itex] but I'm still not sure what to compare it to.
     
  5. Apr 17, 2014 #4

    SammyS

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    Let's see ...

    ## \sqrt{n+1}\ \ > \sqrt{n} ##

    How can that help ?
     
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