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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 120

http://www.youtube.com/watch?v=hBW4S9xcTOk

This 12 year-old is asked to prove the convergence of the following...

Just looking at this.. since sin and cos vary between -1 and 1 there doesn't seem to be any way for this series to converge.

Any thoughts?

*Last edited by Fruityloop (2013-09-06 13:24:05)*

The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

You are right, it's a periodic function, hence does not converge.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi Fruityloop;

I do not believe that converges.

I also do not like him using the integral test which is only for series with positive terms that are monotone decreasing. This series does not apply.

Please take a look at these comments from one of the geniuses that come in here everyday.

http://www.mathisfunforum.com/viewtopic … 21#p258621

Post #22 onwards.

**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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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

What a charming little tyke. Isn't he adorable?

I noticed his IQ was higher than yours m.

I sure wished they had let him go on trying to prove that sum is convergent

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

bobbym wrote:

geniuses that come in here everyday.

Oh wow! Now I have a swollen head. Anyways, look at this: http://www.thescienceforum.com/physics/22406-does-jake-barnett-know-what-hes-talking-about.html

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

He certainly is a busy little guy. You can not have a swollen melon.

I noticed his IQ was higher than yours m.

Yea, but I am better looking.

**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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bobbym wrote:

Yea, but I am better looking.

Why should that count?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

It does not count. I was making a little joke and perhaps responding to the comment.

**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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Ok.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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seems complex and even complicated

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

And funny too, don't you think?

Did you watch the video of Jake?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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No.

I'm actually confused about the whole thread

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

What is confusing to you?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

The fact is Jacob Barnett is a fake, immature, glory-seeking and spoiled child.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

I thought his parents were kind of smug.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

Look at this: now the wikipedia page identifies Barnett as a child prodigy.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

I rather like this kid instead.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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