Solution: Let n, n+1, n+2 be three consecutive positive integers.
We know that n is of the form 3q, 3q+1, or 3q+2.
So ,we have the following cases.
Case1: When n=3q
In this case , n divisible by 3 but n+1 and n+2 are not divisible by 3.
Case2: when n=3q+1
in this case,n+2=3q+1+2 =3(q+1) is divisible by 3 but n and n+1 are not divisible by 3
Case3: when n=3q+2
in this case ,n+1=3q+2+1=3(q+1) is divisible by 3 but n and n+2 are not divisible by 3.
Hence , one of n, n+1 and n+2 divisible by 3