Question

The product of two consecutive positive integers is always divisible by _____​

Answer 1

Answer:

The product of k consecutive positive integers is divisible by n for each positive integer n<=k

Answer 2

Let the 2 consecutive numbers be, x,x+1

product of these consecutive numbers, =x(x+1)

(1) even

let, x=2k

product =2k[2k+1]

from above equation it is clear that the product is divisible by 2

(2) odd

let, x=2k+1

product =(2k+1)[(2k+1)+1]

=2(2k

2

+3k+1)

From above equation it is clear that the product is divisible by 2.