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Homework Help: Simple series question.

  1. Nov 1, 2007 #1
    Determine whether the series [tex]\sum_{n=2}^{\infty}a_n[/tex] converges absolutely,converges conditionally or diverges.If

    [tex]a_n=\frac{1+n+n^2}{\sqrt{1+n^2+n^6}}[/tex]


    For several n I get [tex]a_n>\frac{1}{n}[/tex] so I decided that this series is divergent.Right?
     
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  3. Nov 1, 2007 #2

    Dick

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    That would do it. But did you prove that inequality? Just looking at 'several n' basically means you are guessing.
     
  4. Nov 2, 2007 #3

    Gib Z

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    In fact the result can be much weaker, we don't need to prove the inequality for all n, or even that a_n is more than 1/n, just equal. Divide the terms through by n^2 and see what the n-th term as n --> infinity is.
     
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