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) = 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 MathematicsRD Sharma (2016)Standard X

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