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
Answer:
n(n-1) is even for all integers.
Step-by-step explanation:
We have:
[tex]n(n-1)[/tex]
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.
