Question

the product of two consecutive positive integer is divisible by 2 is this statement true or false give reason

Answer 1

Let the two consecutive positive integers be  and 
Product of two consecutive positive integers 

Case (i):  is even number
Let 
 
 
              
Hence the product is divisible y 2
Case (ii):  is odd number
Let 
 
 
 
     
Clearly the product is divisible y 2
From the both the cases we can conclude that the product of two consecutive positive integers is divisible by 2.