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#1 2016-08-25 05:50:43

FIREFSS
Member
Registered: 2016-08-25
Posts: 6

How to transform a serie into an equation?

Hello,

I'd like to know how do I transform a serie that repeats n times into an equation.

For example:

Serie: ((((A*T)-S)*T-S)*T-S).... for n times.

For this example i know the equation is:

T^n*A-S*(T^n-1)/(T-1)

equation


What method can I use to do this transformation?
Is there a software that can do this?

So far I'm using Excel and using a formula for n lines to get the result.

Thanks!

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#2 2016-08-25 05:59:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How to transform a serie into an equation?

Hi;

A couple of things first.

That thing you are calling a series looks like the Horner form of a polynomial.

T^n*A-S*(T^n-1)/(T-1)

That is not an equation. An equation has an equal sign.

The last line. Is this what you mean?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-08-25 06:09:53

FIREFSS
Member
Registered: 2016-08-25
Posts: 6

Re: How to transform a serie into an equation?

Sorry about the misnaming.

The equal sign wold be the "result" of the polynomial. (Let's call it "R").

Then it wold be like this:

R(n)=((((A*T)-S)*T-S)*T-S).... for n times


and what I wanted to find is this form:

equ

Because this form is much easier to solve for high values of n.

Thanks

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#4 2016-08-25 06:16:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How to transform a serie into an equation?

I imagine the R(1) would be (AT). R(2) = ( (AT)-S)T and R(3) = (((AT)-S)T-S)T? Do I have it right?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2016-08-25 06:24:32

FIREFSS
Member
Registered: 2016-08-25
Posts: 6

Re: How to transform a serie into an equation?

Not exactly. What I mean is:

R(1) = TA-S
R(2) = (TA-S)*T-S
R(3) = ((TA-S)*T-S)*T-S

Sorry if I expressed it wrong.

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#6 2016-08-25 06:28:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How to transform a serie into an equation?

No problem, the problem is with me, I am trying to get us lined up correctly so that we are working on the same thing.

Very likely, Mathematica or any CAS will be able to help you. I will see if I can come up with a method that gets your answer for this example you posted. Hopefully then, this method will be able to do others too.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2016-08-25 06:37:55

FIREFSS
Member
Registered: 2016-08-25
Posts: 6

Re: How to transform a serie into an equation?

Ok, thank you very much!

I'll check if I find a way with Mathematica.

If you come with a method I'd be very pleased to see it, and try to apply it to other cases.

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#8 2016-08-25 07:06:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How to transform a serie into an equation?

Hi;

I can solve for your example. I am getting,

and there is a good method.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2016-08-25 08:47:28

FIREFSS
Member
Registered: 2016-08-25
Posts: 6

Re: How to transform a serie into an equation?

Nice, this equation does the job as I wanted.

If you could share the method you use I would really appreciate.

thanks

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#10 2016-08-25 10:57:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How to transform a serie into an equation?

If you could share the method you use I would really appreciate.

I'll check if I find a way with Mathematica.


Hi;

I have a question. You mentioned Mathematica. How capable are you with Mathematica?

The solution involves noticing that the recurrence for your problem is

with

This is a linear, non-homogeneous  recurrence and the solution can be achieved in a couple of ways. Each, will be tricky. If you are interested in the method of the solutions then we can go over that. But if you are interested in some larger problem and this is just a small piece of that, then the solution methods will just be a nuisance. In this case an automated solution is more to the point.

The following code will solve the problem quickly and accurately:

RSolve[{R[n + 1] == T*R[n] - S, R[1] == T*A - S}, R[n], n] // TraditionalForm

Where do we go from here

It should be obvious that you are not entirely off the hook. We can automate part of the process but unless each of your problems is of this type you will have to find a different recurrence equation for each one. Once you have found it, then Mathematica can be brought to bear.

This is not to say that we can not use Mathematica for finding the recurrence... we can! But until I know more about what your needs are I am stopping right here.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2016-08-25 13:19:25

FIREFSS
Member
Registered: 2016-08-25
Posts: 6

Re: How to transform a serie into an equation?

That's what I wanted to find. The automated solution is perfect.

Only instead of using Mathematica (don't have it here at home), I used WolframAlpha online.

But it worked.
For other similar cases as well.

Thank you!

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#12 2016-08-25 13:46:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How to transform a serie into an equation?

You are welcome.

Come back if you need more and welcome to the forum.

Remember to check the answers those blasted computers give us. Sometimes, they like to taunt us and spit out wrong answers. They seem to know we are inferior and that we will soon be extinct.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2016-08-25 17:12:10

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: How to transform a serie into an equation?

Hi FIREFSS,
The required expression can be derived analytically easily in this case but it can not be generalized.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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