Question

Is n(n - 1) odd or even

Answer 1

Answer:

n(n-1) is even for all integers.

Step-by-step explanation:

We have:

$n(n-1)$

And we would like to determine its parity.

Case 1: n is Even:

If n is even, then we will have an even number (n) multiplied by an odd number (n-1).

Since anything multiplied by an even number is even, n(n-1) is even for all even values.

Care 2: n is Odd:

If n is odd, then we will still have an odd number (n) multiplied by an even number (n-1).

And again, this will yield an even number.

Therefore, n(n-1) will be even for all integers.  

Answer 2

Answer:

n – 1 is an odd integer. Since subtraction rules for even and odd integers are the same as addition rules for even and odd integers, we know that if n – 1 is odd, then n itself must be even, and hence n + 1 must also be odd