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## #10301 2013-04-20 07:24:48

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

It's possible that they have run into him already. Maybe that's why H was locked up, nobody believed what she saw.

## #10302 2013-04-20 07:26:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

Well, he seems to have his own girlfriend and he looks like he has a big crush on her.

What did she see?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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## #10303 2013-04-20 07:50:17

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Nothing, I was joking.

## #10304 2013-04-20 10:59:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

Anyway, how are the questions coming?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10305 2013-04-20 11:01:57

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I did my 270th today, but I have to stop for a bit to do some other work, annoyingly.

## #10306 2013-04-20 11:04:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

270! Very good.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10307 2013-04-20 11:07:22

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I wanted to complete all of them but I don't think that's possible now! It's tempting just to jump to solutions...

## #10308 2013-04-20 11:08:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

That is not a bad idea when you have little time left.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10309 2013-04-20 20:51:34

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Trouble is, even understanding the solutions can be difficult sometimes, as we saw with the cakes question.

## #10310 2013-04-20 23:38:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

It is better than not seeing the solution at all. Sometimes you see a solution and it takes a long time before you understand it.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10311 2013-04-21 02:11:36

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Yes, I have found that to be true, particularly for STEP.

I am stuck on another question...

Find

giving your answer in terms of the tangent of a single angle.

This is the first part of STEP I 1987 Q7.

I remembered this Fourier series:

If you differentiate that, multiply both sides by -1, you get

I thought plugging in x = 2pi/23 might help, but I just couldn't simplify the RHS to the series they state in the question.

For some reason though, 1/2 tan(pi/23) IS the right answer -- which is what you get when you let x = 2*pi/23.

What can I do here?

## #10312 2013-04-21 02:23:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

Hi;

The identity is true.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10313 2013-04-21 02:26:26

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

But how do I show that it is?

## #10314 2013-04-21 02:27:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

Working on it.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

zetafunc.
Guest

Okay, thank you.

## #10316 2013-04-21 02:41:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

Okay got that series too.

The question is a partial sum while you are trying to use an infinite series on the RHS.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10317 2013-04-21 02:55:45

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Yes, I remembered it from a post of yours almost 2 years ago.

## #10318 2013-04-21 02:56:33

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I was hoping to somehow show that the infinite sum on the RHS converged to the sum given in the question...

## #10319 2013-04-21 02:57:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

How are we supposed to change the infinite series we get to the partial sum in the question?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10320 2013-04-21 03:01:22

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Not sure, I thought I could simplify the infinite sum somehow, such that I'd find lots of the terms cancelled and left the sum given in the question.

## #10321 2013-04-21 03:08:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

I am not seeing any way to do that.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10322 2013-04-21 03:14:02

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I couldn't either -- the RHS doesn't converge to that sum.

Will have to think up another way. There is a method on TSR, but it looks long.

## #10323 2013-04-21 03:19:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

I am looking at it now. I do not get it.

I am noticing one thing now, the original question posted is not complete. The series could go one more term and still be true!

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

## #10324 2013-04-21 03:26:25

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

It doesn't -- the sum I posted is definitely what appears on the paper. sin(46pi/23) is also zero.

## #10325 2013-04-21 03:35:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

### Re: Linear Interpolation FP1 Formula

Yes, I was just remarking that the next term also works. This is as you say due to the fact that it is a multiple of 23.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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