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Show that the series is absolutely convergent

  1. Apr 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that
    ##\sum \frac {cos(\frac{n\pi} {3})} {n^2}##
    is absolutely convergent, and therefore convergent

    2. Relevant equations
    Comparison test to 1/n^2

    3. The attempt at a solution
    So to be absulutely convergent the absolute value of the series needs to be convergent. So we compare to the series 1/n^2

    ##\frac {|cos(\frac{n\pi} {3})|} {n^2}/\frac{1}{n^2}##

    so we take the limit as n approaches infinity of

    ##|cos(\frac{n\pi} {3})|##

    And that's where I get stuck because the limit doesn't exist. I know this isn't a trick question because the professor is fair and let us know he wouldn't put anything to trick us on this assignment.

    Where did I go wrong or go from here?
  2. jcsd
  3. Apr 29, 2015 #2


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  4. Apr 29, 2015 #3
    Got it. I thought maybe I could just stop with that but I had so much space on the page I'm thinking, "that can't be all." But yeah. That was my confusion.
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