Question

9. Prove that the product of three consecutive positive integers is divisible by 6.

Answer 1

let the no. be n ,n+1,n+2

multiply all three (n²+n)(n+2)

=n³+2n²+n²+2n

=n³+3n²+2n

=n(n²+3n+2)

=n(n²+2n+n+2)

=n{n(n+2)+1(n+2)}

which is clearly divisible by 6