Question

Is N² + N always an even number? Explain

Answer 1

Answer:

Yes

Step-by-step explanation:

Yes.

Let's first start with even numbers. (N - even number)

Any even number squared, is an even number. Then, we add that squared even number to another even number which would give us an even number.

Now, let's see odd numbers.

Any odd number squared would be an odd number. When you add "N", it would be adding an odd number to an odd number, which gives you an even number.

OR

We can start by factoring the expression:

$N^2+N=N(N+1)$

This is essentially multiplying two consecutive numbers, which in turn means that one number has to be even, and one has to be odd. An odd number multiplied by an even number will always be even.