I have the following sequence: $$x_n= y - sgn(x_{n-1}) \cdot |b\cdot x_{n-1} - c|^{0.5}$$ $$x_1=0$$ Is there a way to find $x_n$ without knowing $x_{n-1}$?
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What are $y,x,b,c$? Shouldn't $x_{n-1}$ appear somewhere on the right hand? What's the point of specifying that $x_n=x_n$? – lulu Jul 06 '16 at 16:17
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@lulu Sorry, some formatting issues on my part. $y,b,c$ are arbitrary integer constants. – Nico A Jul 06 '16 at 16:19
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And what's $x$? – lulu Jul 06 '16 at 16:20
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@lulu Wow, I'm really out of sorts today, sorry. I'm copying this over from a language in which I don't have to specify 'x(n-1)', and forgot to add it to the x's. Should be fixed now. – Nico A Jul 06 '16 at 16:22
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Makes sense now...looks like it is eventually periodic (period $2$). Or at least that it converges to a 2-cycle. Not immediately sure why... – lulu Jul 06 '16 at 16:24
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So this is kind of a nested radical. I don't think it's possible to create a compact expression for $x_n$. The limit of the sequence is possilbe to find, on the other hand – Yuriy S Jul 06 '16 at 16:24