Chebyshev's Sum Inequality/Discrete/Also presented as

Chebyshev's Sum Inequality (Discrete): Also presented as
Some sources present Chebyshev's sum inequality as:
 * $\ds n \sum_{k \mathop = 1}^n a_k b_k \ge \paren {\sum_{k \mathop = 1}^n a_k} \paren {\sum_{k \mathop = 1}^n b_k}$

where:
 * $a_1, a_2, \ldots, a_n$ are real numbers such that:
 * $a_1 \ge a_2 \ge \cdots \ge a_n$
 * $b_1, b_2, \ldots, b_n$ are real numbers such that:
 * $b_1 \ge b_2 \ge \cdots \ge b_n$