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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 · 2 years, 11 months ago

please explain some more · 2 years, 11 months ago

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. · 2 years, 11 months ago

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

oh! according to my knowledge $$2!$$$$=$$$$2$$ so what is the relation between the two · 2 years, 11 months ago

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

Okay. · 2 years, 11 months ago

You answered it. · 2 years, 11 months ago

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

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

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