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Can I use the logic?

  1. Apr 14, 2009 #1
    Can I use this logic?

    1. The problem statement, all variables and given/known data

    I'm wondering if I can use this kind of logic to solve:

    [tex]\sum\frac{(n+1)^n}{n^{(n+1)}}[/tex] Converges or diverges

    3. The attempt at a solution

    [tex] \frac{(n+1)^n}{n^{(n+1)}} \geq \frac{(n)^n}{n^{(n+1)}} [/tex]

    And

    [tex] \frac{(n)^n}{n^{(n+1)}} = n [/tex] , which diverges

    Therefor:

    [tex]\sum\frac{(n+1)^n}{n^{(n+1)}}[/tex] Diverges
     
    Last edited: Apr 15, 2009
  2. jcsd
  3. Apr 14, 2009 #2
    Yes. So long as it's true for all n and n > 0.
     
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