Question

the product of two consecutive positive integer is divisible by 2 is this statement is true or false give reason
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Answer 1

Answer:

True, because the product of any two consecutive numbers, say n(n+1) will always be even as one out of n or (n+1) must be even.

Answer 2

Answer:

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Step-by-step explanation:

let the first integer be x

then the second integer shall be x+1

then their product be x(x+1) = x²+x

(i) If x is even

then x = 2k  

∴ x²+x= (2k)²+2k

=4k²+2k

=2(2k²+k)

hence divisible by two.

(ii)Let x be odd.

∴ x= 2k+1

∴ x²+x = (2k+1)²+2k+1

=(2k)²+8k+1+2k+1

=4k²+10k+2

=2(2k²+5k+1)

hence divisible by two

since both of our conditions satisfy the statement, we can say that the product of two consecutive integers is divisible by 2