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#126 2012-04-26 10:50:17

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

Why? Can you show me an example or a proof?


“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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#127 2012-04-26 10:51:42

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

The fact is you have already seen a couple of examples. You just have not yet understood what you saw.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#128 2012-04-26 10:53:51

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

Can you show me one again?

Is it about numerical stability?


“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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#129 2012-04-26 10:56:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

When you are ready to accept it we will continue with that one. After all, it is the best example of itself. Bafflers is where the answers are.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#130 2012-04-26 10:58:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

If I accept it you will explain it to me? Okay.Sure.3**2-2**2<>(3-2)(3+2). Everybody knows that.


“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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#131 2012-04-26 11:01:39

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

Sure.3**2-2**2<>(3-2)(3+2). Everybody knows that

They do!? 5 = 5, does it not?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#132 2012-04-26 11:03:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

But,by what you propose,it is not. That's confusing 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

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#133 2012-04-26 11:08:38

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

What is an identity?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#134 2012-04-26 11:13:01

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

But why do you say that

a**2-b**2<>(a-b)(a+b)

if it is contradictory to the identity you just wrote above.


“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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#135 2012-04-26 11:14:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

What is an identity?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#136 2012-04-26 11:16:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

Something that always holds?


“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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#137 2012-04-26 11:21:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

That is correct. In computational mathematics that is not an identity, in ordinary algebra it is.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#138 2012-04-26 11:22:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

Why is it not an identity in comp. math? Numerical stability?


“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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#139 2012-04-26 11:24:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

Sometimes it has to do with numerical stability and sometimes it does not.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#140 2012-04-26 11:26:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

And when does it not?


“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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#141 2012-04-26 11:31:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

That was first investigated by John Von Neumann. He could not answer it fully and neither can I. Numerical analysis is the study of algorithms like that so called identity.

Incidentally, that integral, Wolfram does not know how to do it either.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#142 2012-04-26 11:33:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

WA didn't calculate the antiderivative. It evaluated it.


“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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#143 2012-04-26 11:35:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

Nope, the last time I used mathematica on it the darn package did not get more than a few digits right!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#144 2012-04-26 11:37:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

How do you know what the digits are?


“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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#145 2012-04-26 11:43:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

That too is done differently in numerical work than in ordinary math. We verify precision not with mathematical proof but by the double digit method or digit agreement between 2 different methods.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#146 2012-04-26 11:47:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

But then to solve a problem like that one you would need ti find 2 methods. That's even harder.


“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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#147 2012-04-26 11:50:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

Who said it was easy and who says it has to be easy. That is another fallacy drummed into students and teachers. They mistakenly believe all problems are solvable in a couple of minutes and a couple of theorems. Just because all the textbook problems are like that. The truth is real world problem are usually not solvable.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#148 2012-04-26 12:52:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,879

Re: Find the general term!!!

The truth they are hiding is that they are solvable in one command!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#149 2012-04-26 12:57:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

Nice work. Just,hide it please.


“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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#150 2012-04-28 09:24:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Find the general term!!!

#7)Find the generating function and general term (if they exist) of the sequence:

0
1
3
4
6
7
...
...
...
With the obvious increasin pattern +1,+2,+1,+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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