PROVE THAT THE PRODUCT OF THREE CONSECUTIVE POSITIVE INTEGER IS DIVISIBLE BY 6.

Asked by rushi chincholkar | 1st Jun, 2013, 07:39: PM

Expert Answer:

The trick to solve this question is to first apply Euclid's division lemma. From that you will obtain that any positive integer is of the form 6q, 6q+1, 6q+2, 6q+3, 6q+4 or 6q+5.
 
Now, one by one take n equal to above expressions and then prove that product of three consecutive integers is divisible by 6.
Or in other words prove that n(n+1)(n+2) = 6m where m is an integer.

Answered by  | 1st Jun, 2013, 10:26: PM

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