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Suppose that , a_{n+1}=a_n^2-2 and g_n=\frac{a_1a_2...a_n}{a_{n+1}}.

Evaluate \lim_{n\rightarrow \infty } g_n.

I have seen some information in this link. Besides, the sequence gn seems as a good rational approximation for \sqrt5. I know that the answer is 1, But I can't find any nice solution. Any hint is strongly appreciated.

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# The recurrence relation

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