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## #451 2012-02-20 13:33:36

gAr
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### Re: Limits!

Hi bobbym,

What is the limit of a_n as n approaches infinity, with a being any real number.

"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."

## #452 2012-02-20 13:37:22

bobbym
Administrator

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### Re: Limits!

Very good! You found the link, I was hiding it!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #453 2012-02-20 13:49:00

gAr
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### Re: Limits!

Thanks!
Do you want me to erase the link?

"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."

## #454 2012-02-20 15:16:15

bobbym
Administrator

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### Re: Limits!

No, that is okay. I was just teasing him.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #455 2012-02-20 15:33:29

gAr
Star Member

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### Re: Limits!

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."

## #456 2012-02-20 19:52:58

bobbym
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### Re: Limits!

Hi gAr;

Did you know to do that one before you found the link?

Hi anonimnystefy;

See post #450.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #457 2012-02-20 20:25:30

gAr
Star Member

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### Re: Limits!

Hi bobbym,

I tried for sometime, but didn't get the solution. Then I searched for the link.

"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."

## #458 2012-02-20 20:51:47

bobbym
Administrator

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### Re: Limits!

Hi;

I was unable to get it either.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #459 2012-02-20 21:33:43

gAr
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### Re: Limits!

Summations with flooring and ceiling are a bit difficult for me.

"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."

## #460 2012-02-20 23:16:00

bobbym
Administrator

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### Re: Limits!

I agree, it is very hard to eliminate them.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #461 2012-02-21 01:48:19

anonimnystefy
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### Re: Limits!

hi bobbym

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #462 2012-02-21 04:17:21

bobbym
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### Re: Limits!

Hi;

No problem is too easy!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #463 2012-02-21 04:43:08

anonimnystefy
Real Member

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### Re: Limits!

hi bobbym

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #464 2012-02-21 04:46:28

bobbym
Administrator

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### Re: Limits!

Very good!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #465 2012-02-21 04:49:02

anonimnystefy
Real Member

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### Re: Limits!

hi bobbym

next one?

and if you can,please check my attempt at the series #17 problem.tell me if it's good at all.if not i want to change my direction so that i don't waste my time on wrong attempts.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #466 2012-02-21 04:55:41

bobbym
Administrator

Online

### Re: Limits!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #467 2012-02-21 05:04:44

anonimnystefy
Real Member

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### Re: Limits!

hi bobbym

my new friend Maxima says it's

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #468 2012-02-21 05:12:33

bobbym
Administrator

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### Re: Limits!

What do you say it is?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #469 2012-02-21 05:13:59

anonimnystefy
Real Member

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### Re: Limits!

hi bobbym

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #470 2012-02-21 05:15:43

bobbym
Administrator

Online

### Re: Limits!

How do you go about getting such an answer?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #471 2012-02-21 05:33:29

anonimnystefy
Real Member

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### Re: Limits!

hi bobbym

i'm not sure.maybe because e/x tends to zero when x goes to infinity,and 0^'infinity' tends to zero? i'm just guessing because i tried to do the l'Hopital's rule,but i got some pretty nasty functions.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #472 2012-02-21 05:35:52

bobbym
Administrator

Online

### Re: Limits!

Do you at least have some empirical evidence?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #473 2012-02-21 05:43:50

anonimnystefy
Real Member

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### Re: Limits!

hi bobbym

wolfram won't work it out for x=100 or x=1000. think there's no sense in going larger.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #474 2012-02-21 05:50:03

bobbym
Administrator

Online

### Re: Limits!

Did you know that Maxima can do arithmetic that dwarfs Mathematica's puny efforts.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #475 2012-02-27 03:20:54

anonimnystefy
Real Member

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### Re: Limits!

Hi bobbym

I haven't done this on Maxima yet, but I'm sure that the answer is 0.

maybe another way could be using a substitution y=e^x.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

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