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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Have you checked if it works?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

Hohohohohohoooo, that is a good one. I needed that.

Yes, I did and it seems to work.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Okay. Good. Like you said, you can never trust a CAS.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

What now?

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Can you run a_n/(1/5*(-2)^n+2^(n-1)) for n=1,2,3,... for me and tell me the results?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

Hi;

Yes, but what is the LHS and the initial value?

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

No, I just need the value of that expression for n=1,2,3,... a_n is the sequence we were just working on.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

The best I can do is divide each term of that sequence by the denominator you are providing in #55

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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That is exactly what I want you to do.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

Hi;

Sorry, got delayed.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Are sure you used the denominator I gave you?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Ah, sorry. And what about when the denominator is 2^n-(-2)^(n+1)/5.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Hm, so it is good as an asymptotic form.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, it looks like that. You might play with it a little more for a closed form.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I wonder if there is an application of xor in combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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How did you do with getting a closed form?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I got nowhere.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

Okay, how did you get the asymptotic form?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I just reduced the exact form, thinking that it might be easier to work with if we wanted to get anything more about the sequence.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I do not understand, "reduced the exact form?" You have the exact form?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I used the one you got!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,473

I got? Which, what and where?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

bobbym wrote:

That was the second thing I did.

In chained notation:

M = Newton -> Euler -> Fermat

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