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Partial sum be negative?

  1. Nov 18, 2013 #1
    1. The problem statement, all variables and given/known data

    If you sum this
    from one to infinity.
    Ʃ (cos(1/(n)^2 - cos(1/(n+1)^2)


    2. Relevant equations



    3. The attempt at a solution

    Ʃ (cos(1/(n-1)^2 - cos(1/(n+1)^2)
    This is telescoping if you work that out for the partial nth partial sum you get

    cos(1) - cos(1/(n+1)^2) if you take the limit you get cos(1) -1 which is negative. If you punch it in on wolfram you get the same thing. Can the partial sum be negative ?
     
  2. jcsd
  3. Nov 18, 2013 #2

    LCKurtz

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    Yes.
     
  4. Nov 18, 2013 #3
    Can you elaborate please.
     
  5. Nov 18, 2013 #4

    LCKurtz

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    What's to elaborate? Partial sums can be negative. You are looking at one. Plug in some values of n and see.
     
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