Art of Problem Solving: Introducing Pascal's Triangle

Art of Problem Solving's Richard Rusczyk introduces Pascal's Triangle.

[mrblini]

this guy really knows how to teach, not like those awkward nerd scholar university professors who hate helping out or teaching

[VIRAJBHOSLE]

Thanks for the eye opening revelation! 8 years ago, I came across Pascal's triangle and today I understood its use.

[Kurtlane]

Yup! The great Pascal triangle. I've been working on it for years.

[Know_it]

The “choose concept is very new to me". At what level is it introduced?

[davidpsalmpunzalan]

by the time I started hearing the word "choose", I started to look for the comments lol 😂

[billywilliam]

This guy is funny - I like it. Keep going, Man. Thanks for the clip! It's fun

[MichaelSmith]

Can you explain the notation and relationship of "4 choose 2", etc..?... or provide a term/field/method that I can google.. thanks!

[kripasriram]

What does he mean by 5 choose 2 and how would you be able to identify 5 choose 2

[jessefranckowiak]

Why do AoPS videos have so many dislikes? What are you kids on about

[chleung]

Does it have anything to do with binomial theorem?

[coolmathhaha]

Hi I am a middle school student. I would like to know ways to practice for the MathCounts Competition.

[ssozbyg]

You can git triangle numbers from the triangle: (the ones between |'s are triangle numbers)
1
1 1
1 2 |1|
1 3 |3| 1
1 4 |6| 4 1
and so on... (notice that they are all neatly arranged in a row)
AND if you add each row, you will get 2 ^ row-1:
1 = 2^0
1+1 = 2^1
1+2+1 = 2^2
1+3+3+1 = 2^3...

[reddyvikas]

iam not able to understad this can u explain clearly

[BrianScalise]

2 chose 0??? what does that mean...chose 0?

[The-skillsfx]

totally insane
but dnt get discourage

[wilsonxie]

this guy talks so quiet. Unlike his other videos, it sounds like he didin't have enough sleep.

[nikitagaiduk]

I feel really uncomfortable watching this video somehow

[janschetters]

I do not understand anything of what you are saying. You explain it in a very difficult and odd way I do not see, what you see. Are you smart and I am very stuppid?

[zzzz]

I have to do this for my math project, this is the video it came up for the solution, and I don't get it. well I guess that another term I am gonna fail math because of my stupidity! To be honest, i never got maths, and no mater how much i try I never get it! :'(

[dildobaggins]

This guy talks as if hes solving a mystery...?