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Find the minimal value

  1. Aug 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the minimal value of :
    [tex]^{2009}_{n=0}\sum \left| x-k \right|[/tex]
    Such that x is a real value.




    2. Relevant equations



    3. The attempt at a solution

    x must be the mid pt of sqroot of 2009 and 0
    which is approx 18
     
  2. jcsd
  3. Aug 18, 2009 #2
    Re: Summation

    Any additional information, related equations? Is that the original problem?

    Do you mean:

    [tex]\sum_{k=0}^{2009}|x-k|=|x-0|+|x-1|+|x-2|+...+|x-2009|[/tex] ??

    And why do you think that x must be mind point of [itex]\sqrt{2009}[/itex] and 0?
     
  4. Aug 18, 2009 #3
    Re: Summation


    Nope,the given information is written in my previous post.
    For it says the minimal value, and by taking modulus , it is the distance from x to the root of the varying square root. therefore midpt ought to yield the minimal distance overall.
    Correct me if i am wrong (=
     
  5. Aug 18, 2009 #4
    Re: Summation

    Your original question includes the variables x and k in the absolute value and n as an index of the summation. Is this intentional? Is there any relation between k, n, and x? Over which variable(s) are we minimizing? As stated, there is not sufficient information to help answer your question.

    --Elucidus
     
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