Question 29
$n$ are considered real numbers $a_1, a_2, ..., a_n$, not necessarily different. Let $d$ be the difference between the largest and smallest of them and let $s = \sum_{i\lt j} |a_i - a_j|$.
Show that
$$
(n-1)d \le s \le \frac{n^2 d}{4}
$$
and determine the conditions that these numbers must meet $n$ for each of the equalities to be verified.
Show that
$$
(n-1)d \le s \le \frac{n^2 d}{4}
$$
and determine the conditions that these numbers must meet $n$ for each of the equalities to be verified.