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Convergence or divergence (series)

  1. May 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Ʃ[(-1)^n (cosn)^2]/√n

    3. The attempt at a solution
    i dont have the slightest clue where to start
     
  2. jcsd
  3. May 13, 2012 #2

    sharks

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    Gold Member

    Since this is a series and there is an alternating sign in the consecutive partial sums, you should use the Alternating Series Test.
    [tex]\sum^{\infty}_{n=?}(-1)^n \frac{(\cos n)^2}{√n} [/tex]
    You have not stated the initial value for n.

    The first step: Let [itex]a_n=\frac{(\cos n)^2}{√n}[/itex]. Find the limit and test if it's zero.
    Second step: Is [itex]a_{n+1}\leq a_n[/itex]?
    If both of these conditions are satisfied, then the series converges.
     
    Last edited: May 13, 2012
  4. May 13, 2012 #3
    The initial value for n doesn't matter. It's presumably not zero.
     
  5. May 13, 2012 #4

    sharks

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    Gold Member

    The initial value of n is normally ignored, but stating the latter forms part of the proper notation when writing the series with the summation symbol.
     
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