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Absolute convergence proving that limit =1

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data
    limit as k--> infinity ABS VALUE((cos(pi*k+pi))/(cos(k*pi)))


    2. Relevant equations



    3. The attempt at a solution

    Can someone prove to me why this limit is equal to 1? I have tried several other sources and I have not had any luck.
     
  2. jcsd
  3. Apr 10, 2013 #2

    SammyS

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    If k is an integer, what is cos(πk) ?
     
  4. Apr 11, 2013 #3
    It must alternate between -1 and 1.
     
  5. Apr 11, 2013 #4

    LCKurtz

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    Tried other sources? Have you tried working it yourself? What have you done so far?
     
  6. Apr 11, 2013 #5

    SammyS

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    What is [itex]\displaystyle\ \left|\frac{\pm1}{\pm1}\right|\ ?[/itex]
     
  7. Apr 11, 2013 #6
    I understand now. Thanks :)
     
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