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Sum of Geometric Series with cosine?

  1. Jun 8, 2012 #1
    1. The problem statement, all variables and given/known data
    With a series like:
    pi^(n/2)*cos(n*pi)

    How am I meant to approach this?
    Do I use the Squeeze Theorem?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 8, 2012 #2
    I believe you are trying to find the sum as n->infinity?

    If so, you should start by checking whether the series converges or diverges.
     
  4. Jun 8, 2012 #3
    Hi dan38
    As Infinitum suggested, you probably are looking for convergence/divergence of the serie
    I suppose you are being confused by the cos 'trick'.
    But look at is closely.. what possible values do you have for cos(n∏) ?
    1, -1, 1, -1, ... that is, (-1)^n
    Are you familiar with D'Alembert's rule to decide on convergence ?

    Cheers...
     
  5. Jun 8, 2012 #4
    ah I see
    so then it would become

    (pi)^0.5 * (pi)^n * (-1)^n

    pi^0.5 * ( - pi )^n

    -pi^1.5 * ( - pi )^(n-1)

    Of the form required
    where a = -pi^1.5 and r = -pi

    since r > 1
    then it is divergent?
     
  6. Jun 8, 2012 #5
    Well you're notation is confusing, you are supposed to use absolute values and somehow you get to -∏,
    but yes, you would get to ∏>1 and therefore it diverges

    Cheers...
     
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