- #1
asmani
- 105
- 0
Hi all
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 http://oeis.org/search?q=3,7,47,2207&sort=&language=english&go=Search". Besides, the sequence gn 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.
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 http://oeis.org/search?q=3,7,47,2207&sort=&language=english&go=Search". Besides, the sequence gn 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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