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Homework Help: Convergence/Divergence of Given Series Using Alternating Series test.

  1. Mar 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Determine the convergence or divergence of the series: series from n = 1 to infinity of cos (3npi). ((please rewrite in LaTex... idk how?)).

    3. The attempt at a solution

    I rewrote the series to the following:

    series from n = 1 to infinity of (-1)^n ... because the terms of the above series go to -1, 1, -1, 1, -1.

    The first requirement of the alternative series test, is to take the limit as n approaches infinity of the sequence a(sub n). Is a(sub n) just equal to 1 in this case? Doesn't that mean it diverges by the nth term test for divergence because the limit is 1 and not equal to 0?
  2. jcsd
  3. Mar 26, 2009 #2


    Staff: Mentor

    This is the right test, but you're a little off. Limit of a_n is not 1, nor is it -1; the limit doesn't exist.
  4. Mar 27, 2009 #3
    Thanks Mark44!
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