The product of two consecutive integers is divisible by 2

Asked by admin @ 02/08/2021 in Math viewed by 311 People

the product of two consecutive integers is divisible by 2 . is this statemenr true or false Give a reason

Answered by admin @ 02/08/2021

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

Asked by admin @ 24/08/2021 in Math viewed by 360 persons

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