Question

prove that the product of two consecutive numbers are divisible by 2​

Answer 1

Step-by-step explanation:

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Answer 2

Let, (n – 1) and n be two consecutive positive integers

∴ Their product = n(n – 1) = n² −n

We know that any positive integer is of the form 2q or 2q + 1, for some integer q When n =2q, we have

n² − n = (2q)² − 2 = 4q² − 2q

2q(2q − 1)

Then n²− n is divisible by 2.

When n = 2q + 1, we have

n​² − n = (2q + 1)² − (2q + 1)

= 4q² + 4q + 1 − 2q − 1

= 4q² + 2q

= 2q(2q + 1)

Then n​² − n is divisible by 2. Hence the product of two consecutive positive integers is divisible by 2

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