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

tony123
Member
Registered: 2007-08-03
Posts: 195

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

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.

Why did the vector cross the road?
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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#5 2009-04-25 05:53:15

tony123
Member
Registered: 2007-08-03
Posts: 195

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.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

tony123
Member
Registered: 2007-08-03
Posts: 195

very nice thanks

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

gAr
Member
Registered: 2011-01-09
Posts: 3,481

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."

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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: find sum

the next element is 312211

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