Question

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

Answer 1

`483720`

Explanation:

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`