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 ${n+1 \choose 2}$

#Combinatorics #NumberTheory #NaturalNumbers

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 6 years, 11 months ago

please explain some more

Rishabh Jain - 6 years, 11 months ago

hey @Finn Hulse please answer it !!

Rishabh Jain - 6 years, 11 months ago

Okay.

Finn Hulse - 6 years, 11 months ago

You answered it.

Sharky Kesa - 6 years, 11 months ago

@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 - 6 years, 11 months ago

@Finn Hulse – exactly !!

Rishabh Jain - 6 years, 11 months ago

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

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

Sharky Kesa - 6 years, 11 months ago

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

Finn Hulse - 6 years, 11 months ago

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

Rishabh Jain - 6 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.

Rajen Kapur - 6 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Is it factfactfact ororor fictionfictionfiction ?

Comments

Is it $fact$ $or$ $fiction$ ?