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Question

Prove that the product of two consecutive positive integers is divisible by 2.

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Solution

To Prove: that the product of two consecutive integers is divisible by 2.

Proof: Let n − 1 and n be two consecutive positive integers.

Then their product is n (n − 1) = n2 − n

We know that every positive integer is of the form 2q or 2q + 1 for some integer q.

So let n = 2q

So, n2 − n = (2q)2 − (2q)

Let n = 2q + 1

So, n2 − n = (2q + 1)2 − (2q + 1)

Hence it is proved that that the product of two consecutive integers is divisible by 2


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