Prove that the product of two consecutive natural numbers is even.

Using principle of mathematical induction, prove that the product of two consecutive natural numbers is an even number

Prove that the product of three consecutive natural numbers is always divisible by 6.

Prove that the product of r consecutive natural numbers is always divisible by r!.

Prove that the product of any r consecutive natural number is always divisible by r!.

If 1 is added to the product of two consecutive even natural numbers it is equal to the square of the only odd natural number between them.

If 1 is added to the product of two consecutive odd natural numbers it is equal to the square of the only even natural number between them.

Product of 4 consecutive natural numbers is divisible by

Solve the following problems : The product of two consecutive even natural numbers is 120. Find the numbers.

Prove that product of any r consecutive natural numbers is always divisible by r!.