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#26 2012-03-31 03:40:15

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

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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#27 2012-03-31 04:01:48

bob bundy
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Re: Find the general term!!!

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.  smile

Bob


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

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#28 2012-03-31 04:09:14

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

xaxa xD

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

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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#29 2012-03-31 04:11:25

bob bundy
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Re: Find the general term!!!

But it's the challenge!  smile

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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#30 2012-03-31 04:34:24

anonimnystefy
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From: The Foundation
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Posts: 15,657

Re: Find the general term!!!


#2)Find the general term of the sequence:

and

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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#31 2012-03-31 05:19:32

bob bundy
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Registered: 2010-06-20
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Re: Find the general term!!!

Oh !  dunno

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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#32 2012-03-31 05:20:44

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

hi bob

i think you need to reboot again.

i thought you would be mad at me big_smile


“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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#33 2012-03-31 05:23:08

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

Re: Find the general term!!!

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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#34 2012-03-31 05:26:54

bob bundy
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Posts: 6,528

Re: Find the general term!!!

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


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

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#35 2012-03-31 05:33:04

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

Re: Find the general term!!!

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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#36 2012-03-31 05:33:52

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

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.

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

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#37 2012-03-31 05:37:26

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

Re: Find the general term!!!

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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#38 2012-03-31 05:40:56

bob bundy
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Registered: 2010-06-20
Posts: 6,528

Re: Find the general term!!!

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

I thought it was for the root 5 problem.

Doh!

Bob


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

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#39 2012-03-31 05:47:05

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

Re: Find the general term!!!

Ok!


"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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#40 2012-03-31 05:55:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

hi gAr

a_n=1/n - it converges.


“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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#41 2012-03-31 06:00:01

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

Re: Find the general term!!!

Hi,

a_n=1/n ?
I did not get you.


"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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#42 2012-03-31 06:04:21

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

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


“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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#43 2012-03-31 06:41:34

bob bundy
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Registered: 2010-06-20
Posts: 6,528

Re: Find the general term!!!

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


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

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#44 2012-03-31 06:44:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

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.


“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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#45 2012-03-31 06:56:53

bob bundy
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Registered: 2010-06-20
Posts: 6,528

Re: Find the general term!!!

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


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

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#46 2012-03-31 07:27:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

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)


“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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#47 2012-03-31 18:34:24

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

Re: Find the general term!!!

Hi anonimnystefy,

That's what I answered in #35.


"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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#48 2012-03-31 22:18:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

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,...


“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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#49 2012-03-31 22:29:35

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

Re: Find the general term!!!

Hi,

Ok.


"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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#50 2012-03-31 22:35:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Find the general term!!!

Hi gAr

Yes,but you haven't answered the question!


“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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