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#76 2011-08-04 23:55:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Hi gAr;

I feel 6 and 8 are the easier ones, relatively.

Completed 6, but it was not easy for me. Will post it as soon as I latex it up.


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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#77 2011-08-04 23:59:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Series

hi gAr

the answer would be much prettier if you put 9999 instead of 999.

Last edited by anonimnystefy (2011-08-04 23:59:32)


“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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#78 2011-08-05 00:05:55

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi bobbym,

Okay, let us see.

Hi anonimnystefy,

That answer is pretty enough! The prettiest is only when the upper limit is 'n'. Anyway, good job!


"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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#79 2011-08-05 00:23:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Series

thanks! keep up the good problems.


“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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#80 2011-08-05 00:29:31

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

You're welcome.
There are still some for you to try.


"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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#81 2011-08-05 00:45:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Series

i saw them but they look too hard for 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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#82 2011-08-05 01:25:20

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Some questions just require some transformation, then they easily telescope.


"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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#83 2011-08-05 01:45:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Series

hi gAr


“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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#84 2011-08-05 01:49:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Hi;


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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#85 2011-08-05 01:57:16

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi anonimnystefy,


"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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#86 2011-08-05 01:59:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Hi gAr;

Did you see mine, I nearly ran out of cyber ink. But at least I got a refresher course on the discrete calculus.


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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#87 2011-08-05 02:11:45

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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."

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#88 2011-08-05 02:17:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Hi gAr;


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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#89 2011-08-05 02:27:50

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi,

No problem, counts as another solution. I haven't done a problem on discrete calculus, though!

But it must have cost you much time to type the solution, isn't it?


"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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#90 2011-08-05 02:31:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Hi gAr;

About twice as long as it took to do the problem. Then when I was almost done there was a sign error that almost went undiscovered.


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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#91 2011-08-05 02:35:48

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi,

Okay.


"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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#92 2011-08-05 02:48:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Hi gAr;

Thanks for the problems.


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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#93 2011-08-05 02:49:41

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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."

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#94 2011-08-05 03:03:35

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

9)




"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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#95 2011-08-05 15:24:09

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

10)

Prove that


"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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#96 2011-08-05 16:12:56

reconsideryouranswer
Member
Registered: 2011-05-11
Posts: 172

Re: Series

9)


Signature line:

I wish a had a more interesting signature line.

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#97 2011-08-05 16:43:01

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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."

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#98 2011-08-05 16:46:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: 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.

Offline

#99 2011-08-05 16:59:06

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi bobbym,

Did you? Answer looks awesome!


"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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#100 2011-08-05 17:13:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,478

Re: Series

Not yet gAr, it was the suggestion I was applauding. People taught math today have been so conditioned that trying numbers or even guessing at a solution is somewhat evil. They keep mentioning a few offhand problems where some guy tried a thousand numbers and they worked but failed for the 10 millionth number. What they forget is all the problems ( a far larger number by the way ) where getting a solution to fit 1000 numbers worked!

Experimental play can at least provide insight into what a solution might be. With todays computing power this process is easy.


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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