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_{n1}+\frac{2}{a^2_n2}g_n[/tex] to obtain
[tex]g_n=\frac{a_n^2}{a_n^22}g_{n1}[/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}...
