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Is it \(fact\) \(or\) \(fiction\) ?

Is there any relation between both the given facts or this is coincidence : sum of \(n\) natural numbers i.e. \(\frac { n(n+1) }{ 2 } \) and \({n+1 \choose 2}\)

Note by Rishabh Jain
2 years, 11 months ago

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Yes There is relation between both If n(n+1)/2n When we have to find mean Then its equal to n+1/2 Akansha Pal · 2 years, 11 months ago

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@Akansha Pal please explain some more Rishabh Jain · 2 years, 11 months ago

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Imagine the first one in a line of (n+1) persons saying "Hello" to all the n, second saying to remaining (n-1), third to rest of (n-2) and so on till the last but one says "Hello' to the last one. Total number of "Hello' is a combination term, 2 out of (n+1) as each and every pair said "Hello", which is also the sum of first n natural numbers. Rajen Kapur · 2 years, 11 months ago

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If you factor \(n+1\) choose \(2\) you get \(\dfrac{n(n+1)}{2!}\). Finn Hulse · 2 years, 11 months ago

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@Finn Hulse oh! according to my knowledge \(2!\)\(=\)\(2\) so what is the relation between the two Rishabh Jain · 2 years, 11 months ago

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hey @Finn Hulse please answer it !! Rishabh Jain · 2 years, 11 months ago

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@Rishabh Jain Okay. Finn Hulse · 2 years, 11 months ago

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@Finn Hulse You answered it. Sharky Kesa · 2 years, 11 months ago

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@Sharky Kesa Yeah, I know. But he's looking for a reason aside from the coincidence, like a geometric or combinatorial proof. :P Finn Hulse · 2 years, 11 months ago

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@Finn Hulse No, I quite literally mean you answered the command given by Rishabh.

Quote: 'hey @Finn Hulse please answer it !!' Sharky Kesa · 2 years, 11 months ago

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@Finn Hulse exactly !! Rishabh Jain · 2 years, 11 months ago

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