A recurrence relation

Mentallic

Hmm, after looking at it a bit more I realize it's really not telling us as much as I originally thought.

After solving for g_n in

[tex]g_n=g_{n-1}+\frac{2}{a^2_n-2}g_n[/tex] to obtain

[tex]g_n=\frac{a_n^2}{a_n^2-2}g_{n-1}[/tex]

I was simply arguing that the factor approaches 1 as n gets large, but this doesn't really tell us about the limit of g_n...

Mentallic Recognitions: Homework Help	A recurrence relation Hmm, after looking at it a bit more I realize it's really not telling us as much as I originally thought. After solving for g_n in [tex]g_n=g_{n-1}+\frac{2}{a^2_n-2}g_n[/tex] to obtain [tex]g_n=\frac{a_n^2}{a_n^2-2}g_{n-1}[/tex] I was simply arguing that the factor approaches 1 as n gets large, but this doesn't really tell us about the limit of g_n...