Question

prove that the product of two consecutive integers is divisible by 2​

Answer 1

Answer:

Let the 2 consecutive numbers be, x,x+1

product of these consecutive numbers, =x(x+1)

(1) even

let, x=2k

product =2k[2k+1]

from above equation it is clear that the product is divisible by 2

(2) odd

let, x=2k+1

product =(2k+1)[(2k+1)+1]

=2(2k² +3k+1)

from above equation it is clear that the product is divisible by 2

Step-by-step explanation:

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Answer 2

Let we take the integers be 5&6

product=6*5=30

And 30 is divisible by 2