Question

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

Answer 1

Answer:

It's TRUE! the product of two consecutive integers is divisible by two.

Step-by-step explanation:

The product of two consecutive number always contains one even and one odd number. when an even number is multiplied by an odd number we get an even number that is divisible by 2.

0R

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