What is the minimum of $f(x)=|x-1|+|x-2|+cdots+|x-1391|$ function?

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Answer 1 · 2017-05-30T10:32:41

$483720$

We know that

$sum_(k=1)^(k=1391)abs(x-k) = sum_(k=-695)^(k=695) abs(x-k)$

Now the minimum is located by symmetry, at $x = 0$ so

$min f(x) = f(0)=sum_(k=-695)^(k=695) abs(-k) = 2 xx ((696 xx 695)/2) = 695 xx 696 =483720$

What is the minimum of f(x)=|x-1|+|x-2|+cdots+|x-1391|f(x)=|x-1|+|x-2|+cdots+|x-1391| function?