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Infinite Series Convergence using Comparison Test

  1. Apr 23, 2015 #1
    1. The problem statement, all variables and given/known data

    Determine whether the series is converging or diverging

    2. Relevant equations


    ∑ 1 / (3n +cos2(n))
    n=1


    3. The attempt at a solution

    I used The Comparison Test, I'm just not sure I'm right. Here's what I've got:

    The dominant term in the denominator is is 3n and
    cos2(n) alternates between 0 and 1

    so,

    1 / (3n +cos2(n)) < 1 / 3n

    which is convergent geometric series, since | r | = 1/3 < 1

    And so, 1 / (3n +cos2(n)) is convergent according to the Comparison Test
     
  2. jcsd
  3. Apr 23, 2015 #2
    looks ok to me. actually maybe you should change < to ≤ for when cos2 is zero
     
    Last edited: Apr 23, 2015
  4. Apr 23, 2015 #3
    Thanks. Wasn't sure about the cos2(n) part
     
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