Question

Prove that 6 divides n(n + 1) (2n + 1) where n is any positive integer.


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Answer 1

Answer:

Let's start

We have,  n(n+1)(2n+1)  

Multipling the expression by  4  we have

4(n)(n+1)(2n+1) =>  2(n)2(n+1)(2n+1)  

Or,  2n(2n+2)(2n+1) => 2n(2n+1)(2n+2)  

As we can see they were being three consecutive Number,therefore divisible by  3! But as first one is divisible by  2 and also the last one therefore for one of them is also divisible by  4  

So the product is divisible by  24  and the original number i.e n(n+1)(2n+1) which was multiplied by  4  now can reduced by dividing the last expression but we now able to show that it is divisible by  24/4=6  so  n(n+1)(2n+1)  is divisible by  6

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Answer 2

Answer:

we can take n =2

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