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#1 2009-04-25 16:04:17

tony123
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find sum

Last edited by tony123 (2009-04-25 19:25:36)

 

#2 2009-04-25 17:17:51

Identity
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Re: find sum

Are they primes?

 

#3 2009-04-25 20:44:01

mathsyperson
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Re: find sum

I think it's just a +4, +2, ... pattern on the denominator.

I haven't solved it yet, but it's fairly easy to see that it's somewhere between 0.8 and 1.


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It wanted to be normal.
 

#4 2009-04-25 21:45:57

JaneFairfax
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Re: find sum

tony123 wrote:

You made a little mistake, mate. I think you want to find



The Maclaurin series for
is





Also



Hence


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A: Click here for answer.
 

#5 2009-04-26 03:53:15

tony123
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Re: find sum

JaneFairfax wrote:

tony123 wrote:

You made a little mistake, mate. I think you want to find





no jane


 

#6 2009-04-26 04:19:38

JaneFairfax
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Re: find sum

Then you should have been more clear in the first place. mad


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#7 2009-04-29 01:49:30

bobbym
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Re: find sum

Hi Tony123;

Start by forming the power series:



This will equal the terms of Tony's series if x=1. There are differences of 4 and 2 in the exponents. The expansion:



Has exponents that differ by 2.



Has exponents that differ by 4. To get differences of 4 and 2 we use a



This has the required differences of 4 then 2 in the exponents.
Now I tried to use integration, differentiation or multiplication by x on (B)
to make it look like series (A).
I couldn't. So I tried



This one doesn't have the required 4,2 difference in the exponents so it can't be right.
When I tried:



This looks good. Integrate this series and you get



(C) is series (A). So we have:



Now we need the integral.





with x=1






In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#8 2009-04-29 08:03:24

tony123
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Re: find sum

very nice thanks

 

#9 2009-04-29 11:58:10

bobbym
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Re: find sum

Thanks for posing it. It was really a tough problem.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#10 2011-07-30 02:28:09

gAr
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Re: find sum

Hi,

My method may be the same what bobbym says, but I approached by observing that the series is


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
 

#11 2011-10-07 19:41:45

SeireeIngemia
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Re: find sum

My friend showed me this one the other day and I thought it was fun.

1
11
21
1211
111221
-->What goes here?

Hope its not too easy

 

#12 2011-10-07 20:39:34

bobbym
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Re: find sum

Hi SeireeIngemia;

Please start a new thread instead of tacking on to an earlier question for new problems. That way they get the attention they deserve.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#13 2011-10-08 00:10:41

anonimnystefy
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Re: find sum

the next element is 312211


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

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