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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

Nothing, I was joking.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Anyway, how are the questions coming?

**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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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

270! Very good.

**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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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

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.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Hi;

The identity is true.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

But how do I show that it is?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Working on it.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Okay, thank you.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Okay got that series too.

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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

**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

I am not seeing any way to do that.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

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!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

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.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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