The above Question can also be solved in the following way
For any positive integer n,
prove that n3 – n is divisible by 6.
Hint : n3 – n = n
(n2 – 1)
(n – 1)
= n
=
(n + 1)
(n)
……..Since, (a2 – b2) = (a – b)(a + b)
•
Q.
(n + 1)
(n – 1)
Prove that product of three consecutive positive integers is divisible by 6.
Q.
Sol.