Math Is Fun Forum

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

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“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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Find the general term!!!

Oh ! 

I'll think about it.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.