Question

prove that the product of two consecutie integers is alwas divisibele by 2​

Answer 1

Answer:

=k⇒n(n+1)=2k. ... Hence n(n+1) = 2((2q+1)(q+1)), which is even. Hence n(n+1) is always even. Hence the product of two consecutive integers is always divisible by 2.

Answer 2

Answer:

Let the consecutive numbers be x,x+1

In 2 consecutive numbers 1 number is odd and 1 is even

Let x be even

Let x+1 be odd

Product

x(x+1)

x^2+x is divisible by 2

Since,the square of even number is always an even number and sum of 2 even numbers is always even.

Hence Verified.....