Min. Value of Absolutes
Algebra
Level
3
For real number , find the minimum value of the expression above.
The answer is 2500.
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1 solution
The minimum sum occurs when x equals the median of the first 1 0 0 natural numbers ⇒ x = 5 0 . 5 . This gives us:
S M I N = Σ k = 1 1 0 0 ∣ 5 0 . 5 − k ∣ = 2 5 0 0 .
Here's a proof of this minimum absolute-value sum from the Purdue University "Problem of the Week" series.