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Proving Whether an Alternating Series is Divergent or Convergent

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data


    Determine an explicit function for this sequence and determine whether it is convergent.

    an={1, 0, -1, 0, 1, 0, -1, 0, 1, ...}


    3. The attempt at a solution

    I came up with this function:

    an = cos(nπ/2), and wrote that as sigma notation from n=0 to infinity. Is that good or should I use a quadratic?

    I don't think it converges because it just oscillates and never changes, but how do I prove that?
     
  2. jcsd
  3. Nov 3, 2012 #2

    micromass

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    Do you have to prove it using epsilon's and stuff??
    If so, what is the definition of convergence? What is the negation?
     
  4. Nov 3, 2012 #3
    see answer 5
     
    Last edited: Nov 3, 2012
  5. Nov 3, 2012 #4
    I don't have to use epsilons. But I have to provide an equation showing it. And is the function I made satisfactory, or should I express it as a quadratic?
     
  6. Nov 3, 2012 #5
    This sequence has 3 different limit points -1,0 and 1, therefore it does not have a limit.
     
  7. Nov 3, 2012 #6
    If you reffer to the corresponding series,then it diverges because the general term does not converge to 0.
     
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