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Homework Help: Comparison Test

  1. Apr 29, 2005 #1
    Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test.

    [tex]\sum_{n=1}^\infty \frac{2n^4}{n^5+7}[/tex] this diverges using the p-series and comparison test right? p <1


    [tex]\sum_{n=1}^\infty \frac{2n^4}{n^9+7}[/tex] and this converges right? because p > 1



    [tex]\sum_{n=1}^\infty \frac{-1^n}{9n}[/tex] i think this also diverges cause p <1. (not sure about this one)

    can someone check these real quick and tell me if im correct?
     
  2. jcsd
  3. Apr 29, 2005 #2
    First one, P = 1, it diverges.

    2 is correct.

    Hint for the last one

    [tex] \sum_{n=1}^{\infty} - \frac{1^n}{9n} [/tex]

    Whats [itex] 1^n [/itex] for positive n? It should be easy after that.
     
  4. Apr 29, 2005 #3

    HallsofIvy

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    I suspect he meant [tex] \sum_{n=1}^{\infty} -\frac{(-1)^n}{9n} [/tex] for the last one. That converges because it is an alternating series with terms going to 0.
     
  5. Apr 29, 2005 #4
    I was going to make that suggestion, but since his post mentions the comparison test, I decided that the way he originally posted was likely the way that he meant it (since the comparison test can't be used for conditionally convergent series).
     
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