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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

**X'(y-Xβ)=0**

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**Zmurf****Member**- Registered: 2005-07-31
- Posts: 49

Couldn't that be re-written as:

I havn't had much experience with lim, and can't remember what it signifys. What exactly is your question?

Edit: Upon refreshing my memories with limits (The almighty Wikipedia ) The formula I specified is incorrect. I don't know if you already know what your formula does or not. Could supply a bit more information? As far as I can tell, your forumla is getting as close to zero as possible and then bigger at a slower rate depending on the size of n.

If you were to make n = 900. It would make the sum of:

Where i was increasing from 1 until it reached 900.

*Last edited by Zmurf (2006-05-14 19:18:31)*

*"When subtracted from 180, the sum of the square-root of the two equal angles of an isocoles triangle squared will give the square-root of the remaining angle squared."*

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Good.

The interesting here is that n is in non-trivial place in the sum.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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...I think...:)

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

From Excel. Notice the interesting pattern. This may help us rewrite the equation.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

A plot:

*Last edited by krassi_holmz (2006-05-14 20:28:39)*

IPBLE: Increasing Performance By Lowering Expectations.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

krassi_holmz wrote:

Good.

The interesting here is that n is in non-trivial place in the sum.

Yes, you are smart!

To Zmurf and Krassi:

Originally it's a Rieman Sum, an integration question. So I guess Krassi has used integral.

Original Question:

*Last edited by George,Y (2006-05-15 15:21:13)*

**X'(y-Xβ)=0**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

???

That's A Limit!!!

IPBLE: Increasing Performance By Lowering Expectations.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Yes, and that does return a limit result log2

**X'(y-Xβ)=0**

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**liuv****Member**- Registered: 2006-05-14
- Posts: 29

I'm from Beijing China.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

liuv wrote:

How do you transform it into a Rieman Sum? There is no Δx or another 1/n in it!

The integral is indeed a limit if you admit the property of Delta Function:

where

*Last edited by George,Y (2006-05-20 21:16:17)*

**X'(y-Xβ)=0**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Here's a SUM (I actually need it for a question):

Find:

where P means the prime number set.

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

The sum of the reciprocal of every prime to power n?

Download some primes from here: Prime Number List

Then put into Excel.

For Primes up to 100,000

n=1: 2.705272179

n=2: 0.452246618

n=10: 0.000993604

n=20: 9.53961E-07

So that seems to be heading for 0, but then there are infinitely many primes, not just the 9,500 in the list.

(The "2.70" for n=1 is interesting)

(Here's another thought, it will be less than the same sum over positive integers)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**liuv****Member**- Registered: 2006-05-14
- Posts: 29

oh...my English is poor..so i can not express what i think sometimes.:D but i'm very sure my answer is right.:P

on the image:

*Last edited by liuv (2006-05-21 02:46:48)*

I'm from Beijing China.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Thank you liuv, good shifting! My thought is

for krassi holmz,

you may check out some properties for prime numbers.

PS> how did you put "n->∞" under "lim"?

*Last edited by George,Y (2006-05-22 02:31:16)*

**X'(y-Xβ)=0**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Like that. Basically, put a \ before lim.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Yep.

`\lim_{n \to \infty}`

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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Rob wrote:

but then there are infinitely many primes, not just the 9,500 in the list.

That's my point that you can't compute the lim directly- for different number of the primes you'll get different result.

IPBLE: Increasing Performance By Lowering Expectations.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

thanks a lot!

**X'(y-Xβ)=0**

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