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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

hi bob

Nice work! My formula looks similar to yours in that it uses {a}=a-floor(a) but all three of us got a different formula! That's so cool.

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

Thanks. Now, please stop giving me interesting challenges for a while. I've got a lot of stage equipment to sort out and put away.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

xaxa xD

you don't have to answer them if you don't want to

*Last edited by anonimnystefy (2012-03-31 04:09:41)*

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

But it's the challenge!

Bob and signing off before you sneak in another.

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

#2)Find the general term of the sequence:

*Last edited by anonimnystefy (2012-03-31 04:34:56)*

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

Oh !

I'll think about it.

You may have a long wait ..............

................................................................................................................

................................................................................................................

still thinking

-----------------------------------> ∞

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

hi bob

i think you need to reboot again.

i thought you would be mad at me

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi Bob,

Good to know another nice formula!

Hi anonimnystefy,

G.f's can be used here to solve the recurrence.

"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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

It tends to 2.7912878474779....... as n tends to infinity. (quite quickly)

I don't suppose you would accept

f(n) = 2.791287847 for all n greater than 12, would you? he he!

hi gAr,

where did G(x) come from?

Bob

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi Bob,

Yes, I think the question requires a(n) as n->∞, which is (1+√21)/2

G(x) is just a generating function for the series, chose x as a variable.

"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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

hi gAr

nice work!and thanks for the GF.

did you try yourself at #2?

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy,

You're welcome.

I think there's no closed formula for #2. It converges to a value.

"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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

Oh, the generating function for 3,6,8,16 ......

I thought it was for the root 5 problem.

Doh!

Bob

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Ok!

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

hi gAr

a_n=1/n - it converges.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi,

a_n=1/n ?

I did not get you.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

that's a sequence that is convergent and has a closed form.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

I don't think gAr was saying convergent => no closed form but rather

(i) it has no closed form AND (ii) it is convergent.

Did you just make it up or are you expecting that it has a formula (eg. the book says so)?

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

hi bob

I found that sequence before in a math magazine we get at school and the magazine was asking for a value of convergence.i just took the same sequence and just asked for a closed form.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,303

OK. So maybe it is true that it has no closed form.

Where's bobbym when you need him? I haven't seen him at all today. Hope he is OK.

Do you know how to get the convergence?

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

hi bob

i saw him around noon.yesterday i didn't see him much either.something might be happening with him.

yes,i do,but i don't know if it's mathematically accepted:

s=sqrt(5+sqrt(5+sqrt(...+sqrt(5+sqrt(5)))))

s=sqrt(5+s)

s^2-s-5=0

s= (1+sqrt(21))/2

*Last edited by anonimnystefy (2012-03-31 07:27:22)*

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy,

That's what I answered in #35.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

Hi gAr

yes,but bob asked me if I knew how to find it.

**#3) Find the sum of the first n terms of the sequence:**

**1,11,111,1111,11111,111111,1111111,...**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi,

Ok.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,354

Hi gAr

Yes,but you haven't answered the question!

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