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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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#1 2009-10-25 23:36:05

JaneFairfax
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Interesting pattern


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#2 2009-10-26 00:11:55

JaneFairfax
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Re: Interesting pattern








Hence, if n is the number of 1s,



Now






Thus





Hence we have the required formula

Last edited by JaneFairfax (2009-10-26 00:20:57)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#3 2009-10-26 04:45:25

bobbym
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Re: Interesting pattern

Hi Jane;









Isn't it unfortunate the a_n do not continue a predictable pattern. I know you did not say they did. Just looking at your stuff.

Last edited by bobbym (2009-10-26 04:53:04)


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.
 

#4 2009-10-26 05:37:17

bobbym
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Re: Interesting pattern

Hi Jane;



A recurrence like this, is similar to a full history recurrence. They are easy to solve:

Theorem: Every full history recurrence can be changed into a finite history recurrence by the method of differences.



Form a new recurrence:



Now subtract them and you have a finite history recurrence.

Last edited by bobbym (2009-10-26 08:55:40)


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.
 

#5 2009-10-26 14:46:04

soroban
Power Member

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Re: Interesting pattern

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