Question

N is a positive integer

i) Explain why n(n+1) must be an even number?
ii) Explain why 2n-1 must be an odd number?

Answer 1

n(n+1) will always be an even number, and 2n-1 will always be an odd number.

Step-by-step explanation:

i) To determine whether n(n+1) is even, we need to consider two cases. If n is even, then n+1 is odd, and when an even number is multiplied by an odd number, the result is always even. If n is odd, then n+1 is even, and when an odd number is multiplied by an even number, the result is always even. Therefore, in both cases, n(n+1) is always an even number.

ii) 2n-1 is always an odd number because even when multiplied by 2, n will always be an integer, and subtracting 1 from an even number will always result in an odd number.