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Suppose that [itex]a_1=\sqrt5[/itex], [itex]a_{n+1}=a_n^2-2[/itex] and [itex]g_n=\frac{a_1a_2...a_n}{a_{n+1}}[/itex].

Evaluate [itex]\lim_{n\rightarrow \infty } g_n[/itex].

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

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# A recurrence relation

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