Prove that n^2+n is even

To Prove

n² + n is even ∀ n ∈ Z

Proof

n² + n = n * (n + 1)

For the value of n, we have 2 cases

1. n is even
   If n is even, then n * (n + 1) will also be even since multiplying even number with any integer gives even number.
2. n is odd
   If n is odd, then (n + 1) is even since adding odd number with odd number gives even number. This implies that n * (n + 1) will also be even since multiplying even number with odd number gives even number.

Therefore, we can say that n² + n is even ∀ n ∈ Z.