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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

How do you know that it alternates?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

Because he put that 2013 term there.

*Last edited by ShivamS (2014-05-24 06:15:08)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

David has 2014 dolls. He has to choose odd number of dolls from the collection. Find the last three digits of the number which represents the total number of ways in which he could do this.

The 2014 is constant. The choice is 1,3,5,...

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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bobbym wrote:

how do I compute the last three digits of 2014C1+2013C3+2014C5+...+2014C2013 by hand?

Your second term is 2013C3, that can not be right.

Sorry, my second term is 2014C3

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

Wasted last 5 minutes.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

And you need a hand method?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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I'm sorry

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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bobbym wrote:

And you need a hand method?

I want a by-hand method because i am guaranteed that it exists.

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

I am getting 192 by a program.

*Last edited by ShivamS (2014-05-24 06:17:54)*

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i know that

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

Well, I think it's time for me to go to sleep at 2 in the afternoon. I will try to solve it later.

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Thank You for your time.

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

Good night. I will work on it Agnishom.

**In mathematics, you don't understand things. You just get used to them.**

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

I have the answer for you.

**In mathematics, you don't understand things. You just get used to them.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

bobbym wrote:

Good night

Technically it is the afternoon.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

Yes, sorry. But what does it matter if you are tired.

Theorem:

https://www.proofwiki.org/wiki/Sum_of_O … efficients

So

It is known that

http://www.exploringbinary.com/patterns … rs-of-two/

and that

so 8 x 24 = 192

The last 3 digits are 192 and you are done.

**In mathematics, you don't understand things. You just get used to them.**

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Wait, what has it got to do with 2^10?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

2^2003 * 2^10 = 2^2013

**In mathematics, you don't understand things. You just get used to them.**

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That requires a lot of prerequisite knowledge.

I just talked to Alokananda. Yay!

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

All proofs require a large amount of background knowledge. That is the price you pay for no computation!

**In mathematics, you don't understand things. You just get used to them.**

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**Amrita****Member**- From: Westing's House
- Registered: 2014-04-30
- Posts: 814

Happy Birthday,Alokananda. Wish u a very happy and prosperous life ahead.

**In mathematics the art of proposing a question must be held of higher value than solving it. - Georg Cantor (1845-1918)**

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Did you like the graphics?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,582

Did she like them?

**In mathematics, you don't understand things. You just get used to them.**

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I hope....

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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