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#1 2010-02-01 09:48:13
- John E. Franklin
- Member
- Registered: 2005-08-29
- Posts: 3,588
combinations and pascals triangle
Does anyone remember
this used for anything:
n ( n + 1) / 2
or seeing it come up anywhere.
Last edited by John E. Franklin (2010-02-01 13:05:06)
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#2 2010-02-01 14:50:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: combinations and pascals triangle
Hi John;
For one thing it is:
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2010-02-02 06:17:42
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: combinations and pascals triangle
Oh, I was always wondering what those big parenthesis meant.
Can you give that expression a general name type?
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#4 2010-02-02 07:21:15
- soroban
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- Registered: 2007-03-09
- Posts: 452
Re: combinations and pascals triangle
.; .
. .
. .
.
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#5 2010-02-02 07:37:06
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: combinations and pascals triangle
Thank you very much soroban!!
I greatly appreciate that.
I just got through adding all the numbers from 1 to 100 on
a pad of paper and noticed the same thing!!
Can someone tell me what those big parenthesis are
though that bobbym pointed out?
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#6 2010-02-02 07:39:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: combinations and pascals triangle
Hi soroban;
Cool work, soroban
Hi John;
That big parentheses is big pain in the neck. That denotes the binomial. It is read n + 1 choose 2.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2010-02-03 05:58:57
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: combinations and pascals triangle
Danke! = Thank you!
Last edited by John E. Franklin (2010-02-03 06:01:07)
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#8 2010-02-03 07:51:44
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: combinations and pascals triangle
The easier way of adding the first 100 numbers is to group them like this:
1+2+3+...+98+99+100 = (1+100) + (2+99) + (3+98) + ... = 101+101+101+... = 50*101 = 5050.
The legend goes that Gauss's teacher set the class this problem to keep them quiet for a while, but Gauss discovered that method and had it solved in under a minute.
Why did the vector cross the road?
It wanted to be normal.
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#9 2010-02-03 12:34:09
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: combinations and pascals triangle
Sweet for even numbers!
Now for odd numbers you can group with zero:
0 + 1 + 2 + 3 + 4 + 5 = (0 + 5) + (1 + 4) + (2 + 3) = 3 * 5 = 15
Either way the same formula comes out:
n(n+1)/2
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