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Geek Culture / Predicting Pascal's Triangle

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David T
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Posted: 8th Jul 2004 06:34
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Hi,

It's binomial expansion time :p

Basically when doing differentiation I end up with the following expression:

f(x + deltax) - f(x)


Where f(x) = x^n.

In order to expand that you need either know the value of n or use binomial expansion.

I know the rules of binomial expansions, and how Pascal's triangle gives us the co-efficients of each term. However, I haven't found a way to predict a certain row of pascal's triangle.

Anybody know anything about this? Any useful bits of info?

Thanks

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Jimmy
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Posted: 8th Jul 2004 06:44
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Pascal is a programming language.



Oh and math is a headache

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David T
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Posted: 8th Jul 2004 06:45
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Quote: "Pascal is a programming language"


Correct. It's also a triangle.

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zenassem
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Posted: 8th Jul 2004 07:02 Edited at: 8th Jul 2004 07:02
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It' also a mathematician...


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Jimmy
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Posted: 8th Jul 2004 07:07
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I know it's a triangle, I was just giving you my bit of useless info

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zenassem
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Posted: 8th Jul 2004 07:09 Edited at: 8th Jul 2004 07:09
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Not useless. I love me JIMMY FACTS! more jimmy facts!


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Killswitch
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Posted: 8th Jul 2004 07:09
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Isn't that the triangle with all the ones going down the sides and it has the golden ratio n everything? I was staring at a picture of that in maths today, I could have a look if you like.

~I see one problem with your reasoning: The fact is that is a chicken~
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kevil
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Posted: 8th Jul 2004 07:13
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Uhm, what do you want to know.
If you want to know a NCr b, then I can give you the answer.

In case you don't know what a NCr b means:
row number a of pascal's triangle consists of the values a NCr 0 to a NCr a.

Now a NCr b = a! / (b!*(a-b)!)

And that's what you want to know I think.

Kevil
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Emperor Baal
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Posted: 8th Jul 2004 07:14
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http://mathworld.wolfram.com/PascalsTriangle.html


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Chris K
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Posted: 8th Jul 2004 07:33
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Here's a factorial function:

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David T
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Posted: 9th Jul 2004 03:13
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Hi,

Thanks kevil, that's basically how I eventually did it.

Binomial co-efficients are combinational, so

(n|k) = nCk

nCk = (nPk) / k!

nPk = n! / (n-k)!

so

(n|k) = (n! / (n-k)!) / k!

And that works for pascal's triangle, where n is the row number and k is the item number.

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