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#601 2012-04-10 05:47:22

anonimnystefy
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Re: Oh,Oh,Oh,merry analysis!!!

No.

And what about the integral?


“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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#602 2012-04-10 05:48:26

bobbym
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Re: Oh,Oh,Oh,merry analysis!!!

You have any new ideas on that integral?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#603 2012-04-10 05:58:06

anonimnystefy
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Re: Oh,Oh,Oh,merry analysis!!!

No. I asked my prof if he could do it,and guess what he suggested...trig sub and then IBP. So he wasn't helpful,though I did find more ways to write that same integral.

What about you? Anything new?


“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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#604 2012-04-10 06:03:34

bobbym
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Re: Oh,Oh,Oh,merry analysis!!!

IBP will not get there, your professor is unaware of the complexity of the answer.

I do not have a new idea either. So, here is what I do in these spots. I shelve the problem temporarily and work on something else. There are 2 good reasons for doing this.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#605 2012-04-10 06:07:36

anonimnystefy
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Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

I am aware that he is not aware,but I shall not reveal that to him.

Let me guess one of the reasons-what you start doing then might help you on doing the shelved problem?


“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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#606 2012-04-10 06:10:31

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

Possibly, but there are 2 others.

1)Test gamesmanship also works in everyday matters just as well.

2) Forgetting about the problem temporarily, allows the subconscious mind ( a poor term for something else ) to solve it.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#607 2012-04-10 06:12:57

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Yes,we learned about that second reason in Psych class. The process is called hybernation. It has 3 explanations which I will not state here.


“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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#608 2012-04-10 06:18:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

By the way, I was being funny up there. You have already seen an example of sequence acceleration. That is what the RRA is.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#609 2012-04-10 06:22:59

anonimnystefy
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Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Oh,okay. So that's what you meant by that was fun. I thought it might be it,but with you I can never know.


“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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#610 2012-04-10 07:45:01

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

Want to see another one?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#611 2012-04-10 07:47:00

anonimnystefy
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Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Sure! Why 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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#612 2012-04-10 07:56:04

bobbym
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From: Bumpkinland
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Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

We are asked to get that sum to 10 correct digits. How many terms would we have to sum?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#613 2012-04-10 08:03:29

anonimnystefy
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Registered: 2011-05-23
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Re: Oh,Oh,Oh,merry analysis!!!

I'm on my laptop.

We can use Big Oh to get that easily.The exact sum is

.

Let me type the whole procedure here:


“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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#614 2012-04-10 08:14:19

bobbym
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Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

Forget Big O. We are examining how to get the answers without all that. True we are using toy examples just to learn. Later on there will be examples that you will be able to do that Big O will not be able to touch.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#615 2012-04-10 08:17:33

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Well I thought we could get the first approximation using Big Oh and then use RRA to see how much less we can go.

Last edited by anonimnystefy (2012-04-10 08:17:47)


“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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#616 2012-04-10 08:20:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

Maybe we could. But we are making believe that we are stuck with just a computer to evaluate the sum the hard way. Of course we still want to do the least amount of work possible, there sequence acceleration!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#617 2012-04-10 08:22:46

anonimnystefy
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Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Hi bobbym

We use PSQL? 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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#618 2012-04-10 08:24:57

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

No, to use a PSLQ we need a value first for the sum. This must be done by numerical means to a high accuracy.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#619 2012-04-10 08:45:14

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Like what?


“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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#620 2012-04-10 08:46:47

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

The sum we are working is a alternating series.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#621 2012-04-10 08:50:25

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

So?


“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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#622 2012-04-10 08:54:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

So we need 10 digits to put it into a PSLQ. How many terms must I sum to get those 10 digits?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#623 2012-04-10 11:11:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

I don't know. You said not to use Big Oh!


“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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#624 2012-04-10 11:13:18

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Oh,Oh,Oh,merry analysis!!!

You do not need Big O, remember the Leibniz rule for alternating series.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#625 2012-04-10 11:19:42

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Oh,Oh,Oh,merry analysis!!!

Oh yes! Give me some time to calculate 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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