Question

prove that the product of two consecutive natural number is even​

Answer 1

Step-by-step explanation:

In any two consecutive natural numbers, one must be odd and the other one even. An even number has a factor of 2, hence when multiplied by any other number it will still have that factor of 2, hence it will be even. 2n(2n + 1) = 4n^2 + 2n = 2(2n^2 + n) which is EVEN and we're done!

Answer 2

Answer:

In any two consecutive natural numbers, one must be odd and the other one even. An even number has a factor of 2, hence when multiplied by any other number it will still have that factor of 2, hence it will be even. 2n(2n + 1) = 4n^2 + 2n = 2(2n^2 + n) which is EVEN and we're done!