OT math help.

[George Herold]

Hi all, I was helping my daughter with algebra last night.
One set of problems had you find the generating function for a list of integers.
For instance,
list was 1,4,16,64...
Which I wrote as F = 4*F(n-1), F(1) = 1
The HW started counting at n=1 rather than zero... but that hardly matters.
Now my way to solve this is just to guess at the answer. (not very helpful to my daughter.) So I had her play around with different guesses till we 'found' the answer.
F = 4^(n-1).
But it seems there should be a more formal way to arrive at the answer.
So what is it?
A solution for the above would be fine... or web link, or just tell me what this type of problem is called and I can go find the answer on my own.

Thanks George (and Elsie) H.

 

[George Herold]

On Wednesday, December 18, 2013 7:44:26 PM UTC-5, Tim Wescott wrote:

On Wed, 18 Dec 2013 09:38:41 -0800, George Herold wrote:
On Wednesday, December 18, 2013 11:37:51 AM UTC-5, Phil Hobbs wrote:
The problem doesn't have a unique solution unless you possess the
entire list, or a rule for generating the list. For instance,

F = 4**(n-1)+(n-1)(n-2)(n-3)(n-4)*n!


That matches the terms given, but grows a lot faster than 4**N.

Since there's no unique solution given any finite list, it's a
heuristic problem rather than a strictly mathematical one.
Phil, do you every get the feeling that you're too smart for your ow
good?
(He asked with a smile on his face.)

Did you miss the three little dots? 16,64... so 256, 1024... (etc.)

1, 4, 16, 64, 42, ...

x_n = 4 * x_{n-1) - 86 x_{n-4}

So there.

Feeling chastised.
Lowers head, kicks dirt with shoe, "Sorry guys".

(I just hope they don't see the little smirk on my face :^)

George H.

--



Tim Wescott

Wescott Design Services

http://www.wescottdesign.com

 

[George Herold]

On Thursday, December 19, 2013 11:47:13 AM UTC-5, Jim Thompson wrote:

On Wed, 18 Dec 2013 07:27:22 -0800 (PST), George Herold

gherold@teachspin.com> wrote:



Hi all, I was helping my daughter with algebra last night.

One set of problems had you find the generating function for a list of integers.

For instance,

list was 1,4,16,64...

Which I wrote as F = 4*F(n-1), F(1) = 1

The HW started counting at n=1 rather than zero... but that hardly matters.

Now my way to solve this is just to guess at the answer. (not very helpful to my daughter.) So I had her play around with different guesses till we 'found' the answer.

F = 4^(n-1).

But it seems there should be a more formal way to arrive at the answer.

So what is it?

A solution for the above would be fine... or web link, or just tell me what this type of problem is called and I can go find the answer on my own.



Thanks George (and Elsie) H.



I remembered this...





http://www.analog-innovations.com/SED/Difference_Equations-Earnshaw.pdf

Interesting. (in a math sort of way) I've never heard of falling factorials.
(or maybe I was asleep that day in class) reminds me of statistics.. I didn't like that course.

George H.

...Jim Thompson

--

| James E.Thompson | mens |

| Analog Innovations | et |

| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |

| San Tan Valley, AZ 85142 Skype: Contacts Only | |

| Voice480)460-2350 Fax: Available upon request | Brass Rat |

| E-mail Icon at http://www.analog-innovations.com | 1962 |



I love to cook with wine. Sometimes I even put it in the food.

 

[Jim Thompson]

On 19 Dec 2013 05:44:53 GMT, Jasen Betts <jasen@xnet.co.nz> wrote:

On 2013-12-18, George Herold <gherold@teachspin.com> wrote:
Hi all, I was helping my daughter with algebra last night.
One set of problems had you find the generating function for a list of integers.
For instance,
list was 1,4,16,64...
Which I wrote as F = 4*F(n-1), F(1) = 1
The HW started counting at n=1 rather than zero... but that hardly matters.
Now my way to solve this is just to guess at the answer. (not very helpful to my daughter.) So I had her play around with different guesses till we 'found' the answer.
F = 4^(n-1).
But it seems there should be a more formal way to arrive at the answer.
So what is it?


The "easy" way to automate it is to find a polynomial
solution by means on simultaneousl equations.

That won't find 4^(n-1) but something else that fits those points.



the other way is to type them into google, with quotes around them
you'll get a result from OEIS

I remeber being given sequences like this 4,3,3,5,4,4,3,5,5,4,3,6,6,8
or 7,8,4,5,3,4,4 in highschool.. I suspect these where put on the end keep the
fast students quiet.

And those points only... NOT the whole sequence. Sheeeesh!

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[Jim Thompson]

On Wed, 18 Dec 2013 07:27:22 -0800 (PST), George Herold
<gherold@teachspin.com> wrote:

Hi all, I was helping my daughter with algebra last night.
One set of problems had you find the generating function for a list of integers.
For instance,
list was 1,4,16,64...
Which I wrote as F = 4*F(n-1), F(1) = 1
The HW started counting at n=1 rather than zero... but that hardly matters.
Now my way to solve this is just to guess at the answer. (not very helpful to my daughter.) So I had her play around with different guesses till we 'found' the answer.
F = 4^(n-1).
But it seems there should be a more formal way to arrive at the answer.
So what is it?
A solution for the above would be fine... or web link, or just tell me what this type of problem is called and I can go find the answer on my own.

Thanks George (and Elsie) H.

I remembered this...


<http://www.analog-innovations.com/SED/Difference_Equations-Earnshaw.pdf>

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[Tim Wescott]

On Thu, 19 Dec 2013 07:02:11 -0800, George Herold wrote:

On Wednesday, December 18, 2013 7:44:26 PM UTC-5, Tim Wescott wrote:
On Wed, 18 Dec 2013 09:38:41 -0800, George Herold wrote:
On Wednesday, December 18, 2013 11:37:51 AM UTC-5, Phil Hobbs wrote:
The problem doesn't have a unique solution unless you possess the
entire list, or a rule for generating the list. For instance,

F = 4**(n-1)+(n-1)(n-2)(n-3)(n-4)*n!


That matches the terms given, but grows a lot faster than 4**N.

Since there's no unique solution given any finite list, it's a
heuristic problem rather than a strictly mathematical one.
Phil, do you every get the feeling that you're too smart for your ow
good?
(He asked with a smile on his face.)

Did you miss the three little dots? 16,64... so 256, 1024... (etc.)

1, 4, 16, 64, 42, ...

x_n = 4 * x_{n-1) - 86 x_{n-4}

So there.

Feeling chastised.
Lowers head, kicks dirt with shoe, "Sorry guys".

(I just hope they don't see the little smirk on my face :^)

I was smirking, too.

I think those "complete this series" problems are a good way to develop
mathematical intuition, but they're still under-specified.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com