Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20091025 23:36:05#2 20091026 00:11:55
Re: Interesting patternHence, if n is the number of 1’s, Now Thus Hence we have the required formula Last edited by JaneFairfax (20091026 00:20:57) #3 20091026 04:45:25
Re: Interesting patternHi 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 (20091026 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 20091026 05:37:17
Re: Interesting patternHi 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 (20091026 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. 