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#1 2009-10-25 23:36:05
#2 2009-10-26 00:11:55
- JaneFairfax
- Legendary Member
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Re: Interesting pattern
Hence, if n is the number of 1’s,
Now
Thus
Hence we have the required formula
Last edited by JaneFairfax (2009-10-26 00:20:57)
#3 2009-10-26 04:45:25
- bobbym
- Administrator
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.