Answer with Step-by-step explanation:
Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'
Thus the product of the 2 numbers is given by
[tex]Product=n(n+1)\\\\[/tex]
We know that the sum of 'n' consecutive natural numbers starting from 1 is
[tex]S_n=\frac{n(n+1)}{2}\\\\\therefore n(n+1)=2\times S_n............(i)[/tex]
Thus from equation 'i' we can write
[tex]Product=2\times S_n[/tex]
As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.
