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#1 2006-05-14 18:15:24

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

X'(y-Xβ)=0

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#2 2006-05-14 18:48:40

Zmurf
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Registered: 2005-07-31
Posts: 49

Re: Sum of an Infinite Series

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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#3 2006-05-14 19:33:55

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: Sum of an Infinite Series

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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#4 2006-05-14 19:38:39

krassi_holmz
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Re: Sum of an Infinite Series

...I think...:)

IPBLE:  Increasing Performance By Lowering Expectations.

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#5 2006-05-14 19:49:42

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

Re: Sum of an Infinite Series

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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#6 2006-05-14 20:28:18

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: Sum of an Infinite Series

A plot:

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

IPBLE:  Increasing Performance By Lowering Expectations.

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#7 2006-05-15 02:33:51

George,Y
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Re: Sum of an Infinite Series

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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#8 2006-05-19 00:47:37

krassi_holmz
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Re: Sum of an Infinite Series

???
That's A Limit!!!

IPBLE:  Increasing Performance By Lowering Expectations.

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#9 2006-05-19 03:22:17

George,Y
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Registered: 2006-03-12
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Re: Sum of an Infinite Series

Yes, and that does return a limit result log2

X'(y-Xβ)=0

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#10 2006-05-20 14:51:00

liuv
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Registered: 2006-05-14
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Re: Sum of an Infinite Series

I'm from Beijing China.

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#11 2006-05-20 21:08:57

George,Y
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Registered: 2006-03-12
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Re: Sum of an Infinite Series

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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#12 2006-05-20 22:32:27

krassi_holmz
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Registered: 2005-12-02
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Re: Sum of an Infinite Series

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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#13 2006-05-21 00:18:11

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

Re: Sum of an Infinite Series

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

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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#14 2006-05-21 02:08:35

liuv
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Registered: 2006-05-14
Posts: 29

Re: Sum of an Infinite Series

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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#15 2006-05-22 02:28:11

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

Re: Sum of an Infinite Series

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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#16 2006-05-22 09:21:17

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

Re: Sum of an Infinite Series

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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#17 2006-05-22 23:41:23

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: Sum of an Infinite Series

Yep.

\lim_{n \to \infty}

IPBLE:  Increasing Performance By Lowering Expectations.

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#18 2006-05-22 23:44:29

krassi_holmz
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Registered: 2005-12-02
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Re: Sum of an Infinite Series

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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#19 2006-05-27 22:42:26

George,Y
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Registered: 2006-03-12
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thanks a lot!

X'(y-Xβ)=0

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