User:Colball
Hi, I'm Colball.
You might know me as the founder of AoPS times or the founder of The Cool. The Amazing. The Poll Forum. Anyway, I am going to talk about one of my favorite theorems. It says that . And here are three proofs:
PROOF 1: , Hence
. If you dont get that go to words.Conbine the fractions you get
. Then Multiply:
. Finnaly the
's in the numorator cancel leaving us with
. I think you can finish the proof from there.
PROOF 2: The part refers to an
by
square cut by its diagonal and includes all the squares on the diagonal. The
part refers to an
by
square cut by its diagonal but doesn't include the squares on the diagonal. Putting these together gives us a
by
square.
PROOF 3: We proceed using induction. If , then we have
. Now assume that
works. We prove that
works. We add a
on both sides, such that the left side becomes
and we are done with the third proof.
Now I will talk about myself:
Age:
Joined AoPS: Check my Profile (it's my blog)
FTW rating: Bad
Overall alumus level: 8ish
Gender: Can't tell you, (sorry)
Goals: Make longest AoPS wiki user page.
Goals Report: Almost.
Location: Tucson, AZ
Brothers username: kix
Post count: 58, (it would br more if my mom )