Question

Product of two consecutive positive integers is divisible by 2

Answer 1

USING PMI 
so we have to prove n(n+1) is divisible by 2 where  n ∈ I

for n = 1 

1 x 2 = 2 which is divisible by 2 so we see of n = 1 the statement is true 

so let n(n+1) = 2α ⇒ n² + n = 2α 

so the statement is true if n = n+1 is also divisible by 2 

putting n = n+1 

we get (n+1)(n+2) = n² + n + 2n + 2 = 2α + 2n + 2     (using n² + n = 2α )
                                                    = 2(α + n + 1)

so we see for n = n+1 is also divisible by 2 so the statement product of two consecutive  integers is always divisible by 2 is true