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#1 2009-04-24 18:04:17

tony123
Member
Registered: 2007-08-03
Posts: 189

find sum

Last edited by tony123 (2009-04-24 21:25:36)

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#2 2009-04-24 19:17:51

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: find sum

Are they primes?

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#3 2009-04-24 22:44:01

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

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.

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#4 2009-04-24 23:45:57

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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.

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#5 2009-04-25 05:53:15

tony123
Member
Registered: 2007-08-03
Posts: 189

Re: find sum

JaneFairfax wrote:
tony123 wrote:

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



no jane


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#6 2009-04-25 06:19:38

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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.

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#7 2009-04-28 03:49:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#8 2009-04-28 10:03:24

tony123
Member
Registered: 2007-08-03
Posts: 189

Re: find sum

very nice thanks

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#9 2009-04-28 13:58:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#10 2011-07-29 04:28:09

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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?

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#11 2011-10-06 20:41:45

SeireeIngemia
Banned
Registered: 2011-07-03
Posts: 3

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


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#12 2011-10-06 21:39:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#13 2011-10-07 01:10:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,611

Re: find sum

the next element is 312211


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