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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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.

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TopNewestImagine 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.

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If you factor $n+1$ choose $2$ you get $\dfrac{n(n+1)}{2!}$.

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oh! according to my knowledge $2!$$=$$2$ so what is the relation between the two

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hey @Finn Hulse please answer it !!

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Okay.

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You answered it.

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Quote: 'hey @Finn Hulse please answer it !!'

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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

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please explain some more

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