Question

3. For any positive integer 'n', prove that n? -- n is divisible by 6 (or) show that the
product of any three consecutive positive integers is always divisible by 6
Solution:​

Answer 1

Step-by-step explanation:

To prove:-For any positive integer n, n³-n is divisible by 6.

Proof:-

n³-n

n(n²-1)

n(n+1)(n-1)

(n-1)(n)(n+1)

n-1,n,n+1 are 3 consecutive positive integers.

We know that the product of p consecutive positive integers is divisible by p!.

n-1,n,n+1 are 3 consecutive positive integers

So the product of 3 consecutive positive integers is divisible by 3! or 6.

hence proved