Question

prove that product of two consecutive positive integer divisible by 2

Answer 1

As you know every Even Number is Divisible by 2.
So, When we multiply two consecutive number in which one is even And other is odd whose product comes out to be even, quick is Divisible by 2..
Hope you got your answer.


for mathematical proof refer the solution Above..

Answer 2

Answer:

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Let n and n + 1 are two consecutive positive integer

We know that n is of the form n = 2q and n + 1 = 2q + 1

n (n + 1) = 2q (2q + 1) = 2 (2q2 + q)

Which is divisible by 2

If n = 2q + 1, then

n (n + 1) = (2q + 1) (2q + 2)

= (2q + 1) x 2(q + 1)

= 2(2q + 1)(q + 1)

Which is also divisible by 2

Hence the product of two consecutive positive integers is divisible by 2