Question

[20 POINTS] Why does n squared plus n always add up to an even number?

Answer 1

Answer:

EVEN NUMBERS can be looked at as any number (call it "n"), multiplied by 2. Therefore, all even numbers can be described as 2n. Two even numbers added together can be written as: 2n + 2m, where n and m are the even numbers in question, divided by two. A simple rearranging of the terms above gives: 2n + 2m = 2(n + m). Therefore, any even number plus any other even number will always equal an even number (as the answer you get will always be some number multiplied by two). An odd number can be looked at as an even number with one added to it - e.g. 5 is 4+1. Therefore, if you add two odd numbers together, what you're really doing is adding an even number to another even number, then adding 1 + 1, which is 2, and therefore even. As shown above, adding three even numbers together will always give an even number. QED.