Q. 124.0( 4 Votes )

Prove that

Answer :

Given: - Let n, n + 1, n + 2 are three consecutive positive integers

To prove: - Exactly one out of every 3 consecutive positive integers is divisible by 3.


Proof: - We now that n is of the form


3q, 3q + 1, 3q + 2


1st case: - When n = 3q


Here n is divisible by 3, but n + 1, n + 2 are not divisible by 3


2nd case : - When n = 3q + 1


Here (n + 2) = 3q + 1 + 2


= 3q + 3 = 3 (q + 1)


3(q + 1) is divisible by 3, but n, n + 1 are not divisible by 3


3rd case: - When n = 3q + 2


Here n + 1 = 3q + 2 + 1 = 3q + 3


= 3(q + 1) is divisible by 3, but n, n + 1 are not divisible by 3


Exactly one out of every 3 consecutive positive integers is divisible by 3.


Hence proved.


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