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Determining Divergence or Convergence in Series

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\sum[/tex] (2n[tex]^{2}[/tex]+3n)[tex]/\sqrt{5+n^{5}}[/tex]
    index n=1 to infinity

    2. Relevant equations



    3. The attempt at a solution
    I tried both the Ratio Test (limit as n goes to infinity of a[tex]_{n+1}[/tex][tex]/a_{n}[/tex]) and the Limit comparison test (limit as n goes to infinity of [tex]a_{n}[/tex]/ [tex]b_{n}[/tex]) but wasn't able to come up with the same answer from the two tests. What am I doing wrong?
    Does it converge or diverge? How?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 22, 2008 #2
    try breaking it into 2 pieces and see what you can do with the individual pieces, see if
    [tex]\sum[/tex] (2n[tex]^{2}[/tex])[tex]/\sqrt{5+n^{5}}[/tex]
    converges, if it does then the whole thing does since the 2nd term is smaller, if it doesn't then the whole thing does not converge.
     
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