binomials (1 Viewer)

[clintmyster]

far out its so annoying putting the subscript and superscript that I added wrong, fixed solution though

 

[addikaye03]

My terrible version of Pascal's triangle lol:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

⁵C₃ corresponds to the 3rd co-efficient in the sixth row. It turns out that each term in Pascal's triangle can be expressed in combinatorial form (see your calculator for the combinatorial operation)...observe

⁰C₀
¹C₀ ¹C₁
²C₀ ²C₁ ²C₂
³C₀ ³C₁ ³C₂ ³C₃
⁴C₀ ⁴C₁ ⁴C₂ ⁴C₃ ⁴C₄
⁵C₀ ⁵C₁ ⁵C₂ ⁵C₃ ⁵C₄ ⁵C₅

Note that ⁿC_r = n! / [r!(n - r)!]

Yet another awesome expanation Trebla. Do use some code to write ur answers.. like how do u get indices and subscript? It makes it look so much cleaner.

P.S http://community.boredofstudies.org/showthread.php?p=3981903#post3981903 i got a good Q for someone

 

[Timothy.Siu]

Where did the 'C' come from? =O

5C3=5!/3!(5-3)!

 

[Trebla]

Use _{for subscript and ^{for superscript at the beginning and do the same thing but with a "/" before the sub or sup at the end.}}

 

[addikaye03]

Use _{for subscript and ^{for superscript at the beginning and do the same thing but with a "/" before the sub or sup at the end.}}

_{^{Thanks for that man. Ive always wondered lol}}

 

[lyounamu]

Thanks for that man. Ive always wondered lol

um...I cannot be bothered to write that sup thing everytime I do the working out. Writing that thing will further deteriorate my currently abysmal typing speed.

 

[addikaye03]

um...I cannot be bothered to write that sup thing everytime I do the working out. Writing that thing will further deteriorate my currently abysmal typing speed.

Mine is also terrible. By the time i write up my solutions usually 2 people have already answered lol Trebla must copy and paste them or something cos he is quick at it.

 

[Timothy.Siu]

lol i just type it everytime, gets a bit tedious

 

[lyounamu]

learning maths is so amazingly similar to learning chess...

|R|N|B|Q|K|B|N|R|
|P|P|P|P|P|P|P|P|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|P|P|P|P|P|P|P|P|
|R|N|B|Q|K|B|N|R|

|R|N|B|Q|K|B|N|R|
|P|P|P|P|P|P|P|P|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|_|_|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|B|N|R|

|R|N|B|Q|K|B|N|R|
|P|P|P|P|_|P|P|P|
|_|_|_|_|_|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|_|_|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|B|N|R|

|R|N|B|Q|K|B|N|R|
|P|P|P|P|_|P|P|P|
|_|_|_|_|_|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|B|_|R|

|R|_|B|Q|K|B|N|R|
|P|P|P|P|_|P|P|P|
|_|_|N|_|_|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|B|_|R|

|R|_|B|Q|K|B|N|R|
|P|P|P|P|_|P|P|P|
|_|_|N|_|_|_|_|_|
|_|B|_|_|P|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|_|_|R|

i have gained that little bit of wisdom by learning the nature of the game, which just so happens to reflect the nature of many other things in life

|R|_|B|Q|K|B|N|R|
|_|P|P|P|_|P|P|P|
|P|_|N|_|_|_|_|_|
|_|B|_|_|P|_|_|_|
|_|_|_|_|P|_|_|_|
|_|_|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|_|_|R|

|R|_|B|Q|K|B|N|R|
|_|P|P|P|_|P|P|P|
|P|_|N|_|_|_|_|_|
|_|_|_|_|P|_|_|_|
|B|_|_|_|P|_|_|_|
|_|_|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|_|_|R|

similar to the usefulness of the logical system of mathematics when dealing with "real life" problems, the abstract nature of chess and thought processes involved also applies to many strange and detached real life situations...

|R|_|B|Q|K|B|N|R|
|_|_|P|P|_|P|P|P|
|P|_|N|_|_|_|_|_|
|_|P|_|_|P|_|_|_|
|B|_|_|_|P|_|_|_|
|_|_|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|_|_|R|

|R|_|B|Q|K|B|N|R|
|_|_|P|P|_|P|P|P|
|P|_|N|_|_|_|_|_|
|_|P|_|_|P|_|_|_|
|_|_|_|_|P|_|_|_|
|_|B|_|_|_|N|_|_|
|P|P|P|P|_|P|P|P|
|R|N|B|Q|K|_|_|R|

interesting...

aaaah~ isn't that beautiful?

 

[lyounamu]

not as beautiful as this man:
http://thumbnails.cbsig.net/CBS_Production_TheCW/CBS_Production_TheCW/2008/04/22/Primetime/Gossip_Girl/686/920/gg_int_ed-thumb.jpg

and why arent you doing math extensions for your hsc?

ah, i am blinded by his ultimate beauty!

By the way, I do extension maths - extension 2 maths to be specific.

 

[lyounamu]

awaiting namu's response..

lol

i just started sleeping from like 8pm...with my computer on

yeah, my life is good. cannot get better... *sarcasm*

wait, yesterday was good though, had a 4 hour maths session with mates. maths with friends = best thing in the world....



















um...not really

 

[lyounamu]

await response..

hahaha....I just keep forgetting.

I live in Hornsby. It's a really great town with a great future prospect in some particular industries that seem to be on the rise...btw our town is popular with girls.

 

[Zephyrio]

I thought you lived in Asquith, but meh, close enough.

When I was going to the UNCLE med interview, the distance from Strathfield to Hornsby was surprisingly long.

 

[lyounamu]

I thought you lived in Asquith, but meh, close enough.

When I was going to the UNCLE med interview, the distance from Strathfield to Hornsby was surprisingly long.

Well, you probably thought that from some of my posts where I said my house is actually closer to Asquith Station despite being in Horny.

 

[Pacchiru]

lol

-_-