In this problem, we prove a basic property of consecutive positive integers. We are required to show that the product of any two consecutive positive integers is always divisible by 2.
Question
Prove that the product of two consecutive positive integers is divisible by 2.
Solution (WordPress-Safe with Basic Symbols)
Let the two consecutive positive integers be
n and n + 1, where n is a positive integer.
The product of these two consecutive integers is
n × (n + 1).
Out of any two consecutive integers, one integer must be even.
Since one of the numbers is even, their product
n × (n + 1)
is also even.
Every even number is divisible by 2.
Therefore, the product of two consecutive positive integers is divisible by 2.
Conclusion
Hence, the product of two consecutive positive integers is always divisible by 2.
Hence proved.