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Question

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


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) = n2n

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

So let n = 2q 

So, n2n = (2q)2 − (2q)

Let n = 2q + 1 

So, n2n = (2q + 1)2 − (2q + 1)

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


Mathematics
RD Sharma (2016)
Standard X

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