Find the sum of first by constituent is divisible by 3
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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 (As per Euclid Division Lemma),
So, we have the following
Case I When n=3q
In this case, n is divisible by 3 but n+1 and n+2 are not divisible by 3.
Case II 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.
Case III When n=3q+2
In this case, n+1=3q+1+2=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 is divisible by 3.
Step-by-step explanation:
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