Form an expression to represent the process of adding two numbers and then multiplying the sum by half of itself. Prove algebraically that this value is equal to half the square of the sum of the two numbers.
Answer:
Let the two numbers be \(m\) and \(n\).
Sum of the two numbers \(=\) .
Half of the sum of the two numbers \(=\)
Half of the square of the sum of the two numbers \(=\)
Thus, .