Question

Prove that the product of any two consecutive integers is even

Answer 1

Credit: Luqman Khan

Step-by-step explanation:

n(n+1)

n^2+n

check first case n=1

1+1=2 2(1)

it works for first case

assume true for n=k

k^2+k=2A

check n=k+1

(k+1)^2+(k+1)

k^2+2k+1+k+1

k^2+3k+2

k^2+k+2k+2

2A+2k+2

2(A+K+2)

It works for first case. If it works for n=k, then it also works for n=k+1

Then it is true for all 2 consecutive numbers, by mathematical induction