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

Prove that the product of 2n consecutive negative integers is divisible by (2n)! .

Prove that the product of any k consecutive integers is divisible by k! .

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6. Statement-2: Product of three consecutive integers is divisible by 6.

Prove that the sum of three consecutive even numbers is divisible by 6.

Prove that the sum of the two consecutive odd numbers is divisible by 4.

Find the sum of the first 40 positive integers divisible by 6.

Prove, by Principle of Mathematical Induction, that the sum of the cubes of three consecutive natural numbers is divisible by 9.

Show that the sum of the cubes of any number of consecutive integers is divisible by sum of those integers.

Product of any r consecutive natural numbers is always divisible by :