Question 48
Let $m_1 \lt m_2 \lt \dots \lt m_s$ be a sequence of $s \ge 2$ positive integers, none of which can be written as the sum of (two or more) distinct other numbers in the sequence. For every integer $r$ with $1 \le r \lt s$ prove that $r m_r + m_s \ge (r+1)(s-1)$.