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Determine whether the series is convergent or divergent

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data

    I have to find whether the following is Convergent or Divergent

    ∑ from n = 1 to infinity
    2 / n(2n + 2)^(1/4)

    Actually it's the fourth root, this is just easier to write.

    2. Relevant equations

    According to the front of the sheet it's a quiz on P-Series and Integral Test
    I'm leaning more towards Integral Test.

    3. The attempt at a solution

    Not sure how to go about it, i think i've been looking at them for too long, i can't seem to remember how to do integrals anymore
     
  2. jcsd
  3. Feb 2, 2012 #2

    vela

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    I wouldn't use the integral test.
     
  4. Feb 2, 2012 #3

    HallsofIvy

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    Either one will work. The "P-series" test says that a series of the form [itex]\sum n^p[/itex] will converge if p< 1, diverge if [itex]p\ge 1[/itex]. This is not exactly of that form, but you can use the comparison test also. Can you find a p so that [itex]1/(n(2n+2)^{1/4}< n^p[/itex]? The integral test says that a series [itex]\sum a_n[/itex] converges if the integral [itex]\int_1^\infty a(x)dx[/itex] converges where "a(x)" is just [itex]a_n[/itex] with "n" replaced by "x". Can you integrate
    [tex]\int_1^\infty \frac{1}{x(x+1)}dx[/tex]?
     
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