Question

Prove that `n^2-n` divisible by 2 for every positive integer n.

Answer 1

Step-by-step explanation:

${n}^{2} - n = n(n - 1)$

HERE (n-1)n is a positive even number

Case-1

let n is odd

then n-1 is even

Case-2

let n is even

then n-1 is odd

from case-1 and case-2

n(n-1) is even

hence it is even it is divisible by 2