Question

N is a positive integer.Explain why n(n-1) must be an even number.

Please can someone explain this algebraically.

Answer 1

n and (n - 1) are consecutive integers.

Explanation:

We are given 'n', a positive integer.

This 'n' can either be odd or even.

Case I:

When 'n' is odd

The n - 1 is even.

Note that the product of odd and even is always even. That is the product of n and (n - 1) is even.

Case II:

when 'n' is even

Then n - 1 is odd.

Again, using the similar logic we can say that the product of n and n - 1 should be even because here, 'n - 1' is even and 'n' is odd.