Question

for any positive integer n prove that n3 n is divisible by 6 show that the prouduct of any three consective positive integers is always divisible by 6​

Answer 1

Answer:

n!=n(n-1)(n-2)......×3×2×1

Step-by-step explanation:

To prove:- n³-n is divisible by 6

n³-n=n(n²-1)=n(n+1)(n-1)

n³-n=(n-1)(n)(n+1)

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

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

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

n³-n=(n-1)(n)(n+1)

n³-n is the product of 3 consecutive positive integers.

So n³-n is divisible by 6

hence proved