Question

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

Answer 1

Answer:

n(n+1)=n

2

+1

=((n+1)−1)(n+1)

=(n+1)

2

−(n+1)

So if (n+1) is an even no (n+1)

2

is even and diff of even is always even is (n+1).

If odd then (n+1)

2

is odd and diff of odd is always even

So n(n+1) is always even and divisible by 2

Step-by-step explanation:

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Answer 2

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(2k  

2

+3k+1)

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

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Step-by-step explanation: