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July 17, 2019, 04:21:35 pm

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Toothpaste

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Pascal's triangle
« on: October 31, 2007, 10:03:32 pm »
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I've never learned about Pascal's triangle.

Do I need it?

Ahmad

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« Reply #1 on: October 31, 2007, 10:13:57 pm »
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Not for methods, by the looks of it. Although it's very important in combinatorics, so I would learn it! Try to find some cool identities using it  :wink:
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Khangfu

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« Reply #2 on: October 31, 2007, 10:17:38 pm »
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Who needs pascals when you got the binomial theorem :P

enwiabe

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« Reply #3 on: October 31, 2007, 10:26:56 pm »
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o.O yes you do? I remember pascal's triangle questions last year for when you expand out using the binomial theorem.

Ahmad

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« Reply #4 on: October 31, 2007, 10:30:17 pm »
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Unless you use the algebraic definition of binom..
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.


Toothpaste

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« Reply #5 on: October 31, 2007, 10:35:24 pm »
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Guess what, I've never learned the binomial theorem.

..............





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enwiabe

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« Reply #6 on: October 31, 2007, 10:37:17 pm »
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And that's just one of the reason's why you'll get <40 for Methods. :D

Toothpaste

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« Reply #7 on: October 31, 2007, 10:38:39 pm »
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Yeah, probably. Fuck.

asa.hoshi

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« Reply #8 on: October 31, 2007, 10:40:31 pm »
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dont worry.

if its on exam 1 then u are stuffed...
but if its on exam 2... u have ur calc to calc. it.
I KNOW WHAT YOU DID LAST SUMMER!!

Ahmad

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« Reply #9 on: October 31, 2007, 10:41:59 pm »
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Learn it now, it's nothing huge. It'll take less than half an hour, promise.  :)
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.


Toothpaste

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« Reply #10 on: October 31, 2007, 10:44:16 pm »
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... and I was all set to do absolutely nothing till next Friday.

Collin Li

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« Reply #11 on: October 31, 2007, 11:04:43 pm »
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It's not on the course. You don't need to know how to find the coefficient of x^4 for (3x+2)^7.

Toothpaste

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« Reply #12 on: October 31, 2007, 11:07:24 pm »
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Rejoice!

(But I'll learn it since I don't want to be left out of maths world.)

Collin Li

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« Reply #13 on: October 31, 2007, 11:11:42 pm »
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Quote from: "Toothpick"
Rejoice!

(But I'll learn it since I don't want to be left out of maths world.)


It's pretty simple:

Code: [Select]
  1 1
  1 2 1
 1 3 3 1
1 4 6 4 1
   ...


Notice how the numbers from the row above add up together to give the number below? That is Pascal's triangle.

The binomial theorem links to this by saying that you can generate any number from this triangle using nCr, where:
n = the row, and
r+1 = the column
...on Pascal's triangle.

This links into polynomial expansion:

For example:
(x+a)^3 = x^3 + 3ax^2 + 3a^2x + a^3

Notice the coefficients? (1, 3, 3, 1) This is row 3 of Pascal's triangle, for expanding a polynomial of degree 3.

Now, I think you're clever enough to figure out how to find out the coefficient to x^4 for (2x+3)^7

Toothpaste

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« Reply #14 on: November 01, 2007, 12:01:26 am »
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Hah, thanks!

Hmm..
(2x+3)^7 ..

so the coefficient of x^4 is

(7 C 4) (2x)^4 3^(3)

15120?