What Is the Minimal Value of the Summation Involving Absolute Values?

[icystrike]

Homework Statement

Find the minimal value of :
$$^{2009}_{n=0}\sum \left| x-k \right|$$
Such that x is a real value.

Homework Equations

The Attempt at a Solution

x must be the mid pt of sqroot of 2009 and 0
which is approx 18

 

[Дьявол]

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

Do you mean:

$$\sum_{k=0}^{2009}|x-k|=|x-0|+|x-1|+|x-2|+...+|x-2009|$$ ??

And why do you think that x must be mind point of $\sqrt{2009}$ and 0?

 

[icystrike]

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

Do you mean:

$$\sum_{k=0}^{2009}|x-k|=|x-0|+|x-1|+|x-2|+...+|x-2009|$$ ??

And why do you think that x must be mind point of $\sqrt{2009}$ and 0?

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 (=

 

[Elucidus]

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