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Homework Help: Determine if series converges

  1. Mar 26, 2013 #1
    1. The problem statement, all variables and given/known data
    Determine if series converges or diverges.

    2. Relevant equations
    [itex]\displaystyle \sum^{∞}_{n=0} \frac{cos n* \pi}{5^n}[/itex]

    3. The attempt at a solution
    I have tried using the nth term test but not sure how to take the limit of cosine.
  2. jcsd
  3. Mar 26, 2013 #2


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    Homework Helper

    Why don't you try working out the value of that cosine term for the first few values of n and see what you get?

    Another hint: absolute convergence.
  4. Mar 26, 2013 #3


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    Science Advisor

    First, [itex]cos(n\pi)[/itex] is just [itex](-1)^n[/itex] so this is [itex]\frac{(-1)^n}{5^n}[/itex] and the ratio test works nicely.
  5. Mar 26, 2013 #4


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    Homework Helper

    What is ##\sum |a_n|##, can it be bounded in some way?

    Then perhaps another test will clean the rest up for you.
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