use the root test to determine whether the series convergent or divergent sum of $($n$=1$ to infinity$)(($n$^2+8)/(9$n$^2+2))^$n$.$ identify an$,$ evaluate the following limit lim $($n to infinity $)$ n saurerroo absolute an$.$ SInce lim n to infinity square root $($absolute an$)..\mathrm{.}1,$ the series s$....$