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

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

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

Are they primes?

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

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.

Why did the vector cross the road?

It wanted to be normal.

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

tony123 wrote:

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

The Maclaurin series for

isAlso

Hence

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

JaneFairfax wrote:

tony123 wrote:You made a little mistake, mate. I think you want to find

no jane

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

very nice thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

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

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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."

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

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

Creditors have better memories than debtors. Creditors have better memories than debtors.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

the next element is 312211

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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