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 \({n+1 \choose 2}\)

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TopNewestYes 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 · 3 years, 1 month ago

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– Rishabh Jain · 3 years, 1 month ago

please explain some moreLog in to reply

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 · 3 years, 1 month ago

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If you factor \(n+1\) choose \(2\) you get \(\dfrac{n(n+1)}{2!}\). – Finn Hulse · 3 years, 1 month ago

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– Rishabh Jain · 3 years, 1 month ago

oh! according to my knowledge \(2!\)\(=\)\(2\) so what is the relation between the twoLog in to reply

hey @Finn Hulse please answer it !! – Rishabh Jain · 3 years, 1 month ago

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– Finn Hulse · 3 years, 1 month ago

Okay.Log in to reply

– Sharky Kesa · 3 years, 1 month ago

You answered it.Log in to reply

– Finn Hulse · 3 years, 1 month ago

Yeah, I know. But he's looking for a reason aside from the coincidence, like a geometric or combinatorial proof. :PLog in to reply

Quote: 'hey @Finn Hulse please answer it !!' – Sharky Kesa · 3 years, 1 month ago

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– Rishabh Jain · 3 years, 1 month ago

exactly !!Log in to reply