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If $$\left\{x_{n}\right\}\mid x_{1}=5,x_{n+1}=x_{n}^{2}-2,\forall n\geq 1$$ find $$\lim_{n\to\infty}\frac{x_{n+1}}{x_{1}x_{2}\cdots x_{n}}.$$

If someone could help me out with tags, it'd be lovely. I think this is calculus and real-analysis, but I'm not sure--I had the problem scribbled down on a post-it, and I forget where it's from.

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    The sequence *exists*, since you've defined it recursively. What do you mean by "If ... exists"?2012-03-18
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    The "analysis" tag is for a more abstract question than this one. "calculus" also refers to something else ; elementary limits (of functions, not of sequences), differentiation, elementary optimization, etc. real analysis and sequences are really the tags you want here.2012-03-18
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    @ArturoMagidin Whoops, thanks for the correction.2012-03-18
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    I feel like I've seen this in a putnam exam or something. But I can tell it's just hard.2012-03-18

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