N is a positive integer. Explain why n(n-1) must be an even number.

If N is a positive integer, it must be either even or odd. If N is odd, then N-1 will be even. If N is even, then N-1 will be odd. Either way, when you multiply n and n-1, one of those expressions is going to be an even number, and any number multiplied by an even number is an even number. Hope this helps! :)

Final answer: The expression n(n-1) is always even as one of the numbers n or n-1 is always even and the product of an even number and any other number is always even. Explanation: The expression n(n-1) will be even is because one of any two consecutive integers must be even. This is a fundamental principle of number theory. The product of an even and any other number is always even. Therefore, since n(n-1) is the product of two consecutive integers, it is always even. For example, if n = 3, n-1 = 2, and the product, 6, is even. Learn more about Even Numbers here: brainly.com/question/2289438 #SPJ3