Bitter numerics:

bobbym · 2014-07-01 02:51:55

C is trying to sum a series numerically. Here is the series.

He plows away with his favorite computer language ( C++ I think ) and comes up with 0.691363061604078 after 100000 terms.

E points out to him that there is a way to sum the series using generating functions and that it sums to ln(2).

C is happy, but he notices that his sum only got 2 correct digits and he was not able to guess at the true solution using his answer. C asks our distinguished panel how he could have done better numerically.

A says) I asked my department head and she said get a faster machine and use Micro$oft C.

C says) I tried it to much bigger numbers than 100000 and it still had trouble even getting 3 digits. I do not think a faster machine is the answer.

B says) You could have got much more accuracy with less terms using

A says) Now hold on B! You are not going to throw some of that computer garbage around are you? My department head makes 4 times what you do so she has to be right. You listen to me C!

D says) What is a department head?

E says) I can not believe that they let A on this panel. Why are you here?

A says) Genetics baby, pure and simple. Mine are better!

Can you help C with a numerical solution that will agree with log(2). Remember he wants a computer solution.

gAr · 2014-07-05 20:50:45

Hi bobbym,

bobbym · 2014-07-05 22:25:13

Hi;

gAr · 2014-07-05 23:11:21

Hi,

Thanks!
What transform did you apply?

bobbym · 2014-07-05 23:17:03

Hi;

gAr · 2014-07-05 23:28:26

Okay.
Thanks for the problem, I could not have found it otherwise.
Now I can simply use that program as a template for any series I meet!

Agnishom · 2014-07-05 23:30:29

C can punch this into Mathematica and it will output Log[2]

Last edited by Agnishom (2014-07-05 23:30:53)

bobbym · 2014-07-05 23:33:28

Hi;

That is correct but C needs another type of solution.

Agnishom · 2014-07-05 23:47:21

Do I have to use C++?

bobbym · 2014-07-05 23:52:32

Any language other than one that can do the sum for you. In other words accelerate convergence. Less terms, more digits. Use the double rule.

Agnishom · 2014-07-06 00:06:06

What rule is that?

bobbym · 2014-07-06 00:09:22

Hmmmm, I see you will require a tutorial.

Agnishom · 2014-07-06 00:43:39

I am ready for the tutorial.

bobbym · 2014-07-06 00:49:26

Start by summing the problem to 100000 terms with your favorite language.

Agnishom · 2014-07-06 01:21:11

My favorite language is bengali!

bobbym · 2014-07-06 01:24:44

Hmmm, then sum it in that.

Agnishom · 2014-07-12 04:41:56

I have written a small routine to do it without acceleration in Maxima but it is taking a lot of time.

bobbym · 2014-07-12 04:45:17

Is that not the point?

David · 2014-07-12 04:48:37

মাত্র একটি ভাষা যথেষ্ট নয়।

bobbym · 2014-07-12 04:55:18

That is true but a little math goes a long way.

Agnishom · 2014-07-12 05:05:24

chooipian wrote:

মাত্র একটি ভাষা যথেষ্ট নয়।

Not enough? You want me to do it in python?

bobbym, so what should I be doing>

bobbym · 2014-07-12 05:16:24

The problem is not in the languages being used. "Get a bigger hammer," is the cudgel not the scalpel.

Here is the cudgel.

Agnishom · 2014-07-12 12:22:55

You do not need a bigger hammer. You need a screw driver, instead

bobbym · 2014-07-12 12:26:05

Did you understand what I meant?

Agnishom · 2014-07-12 12:34:03

Yes

Math Is Fun Forum

#1 2014-07-01 02:51:55

Bitter numerics:

#2 2014-07-05 20:50:45

Re: Bitter numerics:

#3 2014-07-05 22:25:13

Re: Bitter numerics:

#4 2014-07-05 23:11:21

Re: Bitter numerics:

#5 2014-07-05 23:17:03

Re: Bitter numerics:

#6 2014-07-05 23:28:26

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#7 2014-07-05 23:30:29

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#8 2014-07-05 23:33:28

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#9 2014-07-05 23:47:21

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#10 2014-07-05 23:52:32

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#11 2014-07-06 00:06:06

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#12 2014-07-06 00:09:22

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#13 2014-07-06 00:43:39

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#14 2014-07-06 00:49:26

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#15 2014-07-06 01:21:11

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#16 2014-07-06 01:24:44

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#17 2014-07-12 04:41:56

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#18 2014-07-12 04:45:17

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#19 2014-07-12 04:48:37

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#20 2014-07-12 04:55:18

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#21 2014-07-12 05:05:24

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#22 2014-07-12 05:16:24

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#23 2014-07-12 12:22:55

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#24 2014-07-12 12:26:05

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#25 2014-07-12 12:34:03

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