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**BarandaMan****Guest**

Hi,

I have spent SO long on this problem, so much so that it is now 4.04am here in the UK.

I will post the problem, it is not too hard I have been told, I just cannot rearrange it to get the given solution. Please could someone help me?

Here is the picture of the problem that needs to be rearranged (left hand side) and on the right hand side, the eventual answer.

tinypic.com/view.php?pic=bg49hu&s=5

The methods I have tried are:

1. Dividing everything by (Pi/P)^-n

2. Multiplying everything by (Pi/P)^n+1

Please please help me!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

I do remember doing this type problem with you before.

**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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**BarandaMan****Guest**

bobbym wrote:

Hi;

I do remember doing this type problem with you before.

Hello!

I still do not understand it and finals are coming up on Thursday so I am trying it again, but I stll have no idea...:(

**BarandaMan****Guest**

But those two methods are meant to work, or one of them should definitely work, but i always get to a penultimate stage and cannot get further...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

Is that a y after the (Pi - w)? And what is the power of the first term, -n?

**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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**barandaman****Guest**

bobbym wrote:

Hi;

Is that a y after the (Pi - w)? And what is the power of the first term, -n?

Hi bobby!

No that is as n, the same symbol as the power of the first term, which yes is -n,

then the second term is to the power of -n-1.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

This is what we have:

**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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**barandaman****Guest**

bobbym wrote:

Hi;

This is what we have:

Yes! That is exactly what we have at this moment.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

There was one mistake in the way my program did the latexing. This is what you want

one more thing, that Pi is π?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

Hi;

There was one mistake in the way my program did the latexing. This is what you want

one more thing, that Pi is π?

I do apologise for not stating that. That Pi is not actually the greek symbol, it denotes the price level for individual goods (whereas P alone represents the overall price level).

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

2. Multiplying everything by (Pi/P)^(n+1)

That is the correct move.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

Hi;

2. Multiplying everything by (Pi/P)^(n+1)

That is the correct move.

Thank you,

When I divide the first term by it, it becomes simply (Pi/P).

When I divide the second term by it, it becomes: -((Pi-w)n)/P

So (Pi/P) -((Pi-w)n)/P = 0

So (Pi/P) = (nPi/P) (nw/P)

This is where I really do not know how to get this into the correct answer:

(Pi/P)=(W/P)*(n/n-1)

Could you please see where I have gone wrong / how I can continue? Thank you so much

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

When I divide the first term by it, it becomes simply (Pi/P).

When I divide the second term by it, it becomes: -((Pi-w)n)/P

You mean multiply instead of divide, and you are correct up to there.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

Hi;

When I divide the first term by it, it becomes simply (Pi/P).

When I divide the second term by it, it becomes: -((Pi-w)n)/PYou mean multiply instead of divide, and you are correct up to there.

Yes, sorry again. I do mean multiply.

What have I done wrong after? I really do not know what is going on, I have spent hours here.

Alternatively I try multiplying the P across from this step: So (Pi/P) -((Pi-w)n)/P = 0

To get Pi - (Pi-w)/n = 0. Then it leads to the same thing, as I divide by P later to try to get the Pi/P expression. These two ways seem equivalent.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hold on you are going to fast. After the multiplication of the two terms you should have:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

Hold on you are going to fast. After the multiplication of the two terms you should have:

Yes, I have this!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Remember that has a zero on the right so it is really:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

Remember that has a zero on the right so it is really:

Yes! So we can multiply across to rid the P, but then we need to divide again by P to get the required expressions? So there is no need multiplying across?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

No, do not multiply by the P. Instead split the fraction up like this:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

No, do not multiply by the P. Instead split the fraction up like this:

Ok thank you, I have now done that. The only next step I can see is to write (nw/P) + (Pi(1-n)/P)=0.

Then I am stuck again. I am really sorry I am not getting this faster I do apologise

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

Everything is going fine.

These are the two steps so far:

becomes

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

Yes, that is where I am at. At the latter stage, I really have no idea what to do. I tried working backwards from the eventual solution but I can still not see a link.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**barandaman****Guest**

bobbym wrote:

Oh my I think we are close.

So from there, I divide by -1 to get

-Pi(n-1)/P = nw/P

So -Pi/P = nw/(n-1)P, but there is a negative on the LHS which we do not want?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,544

Hi;

We are getting there just a few more steps:

Divide both sides by (1-n)

Now you use the identity:

We are done!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**