Ask a Teacher

Search



prove that the product of 2 consecutive positive integer is divisible by 2.
Let x and y=x+1 be two consecutive integers.then either
x is divisible by 2 or y be divisible by 2.
Let x be divisible by 2.ie,
x=2k
y=2k+1
x*y=2k*(2k+1)
Since 2k is divisible by 2.the above result will be divisible by 2.
Otherwise assume x is not divisible by 2. In this case x = 2k+1,then
y=(2k+1)+1
  =2k+2
  =2(k+1) ,which is divisible by 2.


comments powered by Disqus