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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#26 2011-08-01 20:59:24

gAr
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Re: Series

Hi bobbym,


"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."
 

#27 2011-08-01 21:27:27

bobbym
Administrator

Online

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#28 2011-08-01 21:34:45

gAr
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Re: Series

Hi,


"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."
 

#29 2011-08-01 21:40:21

bobbym
Administrator

Online

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#30 2011-08-01 21:43:36

gAr
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Re: Series

Hi,

You integrated only LHS???!!!


"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."
 

#31 2011-08-01 21:51:07

bobbym
Administrator

Online

Re: Series

Hi gAr;

I forgot that?! But it is not helping, now I am getting pi^3 / 6 for the RHS ( I used a definite integration from 0 to pi )


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#32 2011-08-01 21:52:56

gAr
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Re: Series

Hi bobbym,

Now it's okay.
Remember that there is a pi on the LHS.


"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."
 

#33 2011-08-01 21:56:43

bobbym
Administrator

Online

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#34 2011-08-01 22:00:25

gAr
Star Member

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Re: Series

Hi bobbym,


"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."
 

#35 2011-08-01 22:02:15

bobbym
Administrator

Online

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#36 2011-08-01 22:07:00

gAr
Star Member

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Re: Series

You are welcome!


"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."
 

#37 2011-08-01 22:47:34

bobbym
Administrator

Online

Re: Series

Next ones look tougher!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#38 2011-08-01 22:53:39

gAr
Star Member

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Re: Series

Hi,

Here's a solution



Hi bobbym,

Trigonometric identities will be useful for the other two.
Of course, other methods may be there, I don't know yet!


"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."
 

#39 2011-08-01 23:33:15

bobbym
Administrator

Online

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#40 2011-08-01 23:41:19

gAr
Star Member

Offline

Re: Series


"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."
 

#41 2011-08-01 23:43:10

bobbym
Administrator

Online

Re: Series

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#42 2011-08-01 23:44:23

gAr
Star Member

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Re: Series

Hi,

Which step?


"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."
 

#43 2011-08-01 23:46:50

bobbym
Administrator

Online

Re: Series

Hi gAr;



I can not do this sum!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#44 2011-08-01 23:52:22

gAr
Star Member

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Re: Series

Oh, we are not evaluating there. We substitute for z from the previous step.


"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."
 

#45 2011-08-01 23:55:29

bobbym
Administrator

Online

Re: Series

Hi;

I got it now! Thanks!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#46 2011-08-02 00:00:24

gAr
Star Member

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Re: Series

You're welcome!


"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."
 

#47 2011-08-02 00:08:28

gAr
Star Member

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Re: Series

I see that term by term integration works wonders in some of the cases!

5)

Find


"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."
 

#48 2011-08-02 00:22:01

anonimnystefy
Real Member

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Re: Series

hi gAr

Last edited by anonimnystefy (2011-08-02 00:23:53)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#49 2011-08-02 00:32:08

gAr
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Re: Series

Hi anonimnystefy,

You may try.
But if you try to sum the fractions separately, they both diverge.


"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."
 

#50 2011-08-02 16:56:53

bobbym
Administrator

Online

Re: Series

Hi gAr;

Working on 5), it is a nice one.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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