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

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

### 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
The knowledge of some things as a function of age is a delta function.

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

bob bundy
Registered: 2010-06-20
Posts: 8,075

### 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.

Bob

Children are not defined by school ...........The Fonz
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
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Find the general term!!!

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
The knowledge of some things as a function of age is a delta function.

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

bob bundy
Registered: 2010-06-20
Posts: 8,075

### Re: Find the general term!!!

But it's the challenge!

Bob  and signing off before you sneak in another.

Children are not defined by school ...........The Fonz
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
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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

bob bundy
Registered: 2010-06-20
Posts: 8,075

### Re: Find the general term!!!

Oh !

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

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

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

still thinking

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

Bob

Children are not defined by school ...........The Fonz
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
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Find the general term!!!

hi bob

i think you need to reboot again.

i thought you would be mad at me

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
The knowledge of some things as a function of age is a delta function.

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## #33 2012-03-31 05:23:08

gAr
Member
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
Registered: 2010-06-20
Posts: 8,075

### 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

Children are not defined by school ...........The Fonz
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
Member
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
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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

gAr
Member
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
Registered: 2010-06-20
Posts: 8,075

### 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

Children are not defined by school ...........The Fonz
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
Member
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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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

### 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
The knowledge of some things as a function of age is a delta function.

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## #43 2012-03-31 06:41:34

bob bundy
Registered: 2010-06-20
Posts: 8,075

### 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

Children are not defined by school ...........The Fonz
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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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## #45 2012-03-31 06:56:53

bob bundy
Registered: 2010-06-20
Posts: 8,075

### 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

Children are not defined by school ...........The Fonz
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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

Offline