My Math Forum LIMIT ANALYTHIC OR ROTATION NUMBER?

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 November 2nd, 2010, 06:38 PM #1 Newbie   Joined: Nov 2010 Posts: 1 Thanks: 0 LIMIT ANALYTHIC OR ROTATION NUMBER? The problem is: Let 0 < $\beta$ < 1 be irrational and $s_n := sign (sin(n\pi\beta))$, n=1,2,3... The sequence $w_n := |s_n - s_{n+1}|/2$ detects the sign changes of the sequence s_n. Prove: lim (N --> inf) $\frac{1}{N}\sum_{n=1}^{N} w_n=\beta$ I don't know how to finish the problem analytically! should I use the rotation number? Thanks you so much! Help, please!

 Tags analythic, limit, number, rotation

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