[math]

[math]
{{2n}\choose{2}} = 4{{n}\choose{2}} + n
[/math]
>Veeky Forums can't prove this

>memebinatorics

...

Do your own homework faggot

wrong for n=1

Just did. See

It's not homework, I just stumbled upon it in my imaginings.

I remember I once proved doing something very ingenious.

Fuck induction, induction is for gay boys.

Compute [math] {{2n}\choose{2}} - 4{{n}\choose{2}} [/math]

First apply the definition of choose. Then merge both fractions into one and then use the definition of factorial to cancel a bunch of shit.

I was surprised, but you can actually reach [math] n [/math] if you are clever enough.

Good luck with your homework, Brainletto.

>manipulating symbols
>not double counting

[math]
\sum\limits_{k=1}^{n}k{{n}\choose{k}}=n2^{n-1}
[/math]
>Veeky Forums can't prove this