For the series from 1 to inf of (2n^2 - 1)/(3n^5 + 2n + 1), would it be possible to compare (2n^2 - 1)/(3n^5 + 2n + 1) to 2/3^3 for the limit comparison test?
If you meant 2/n^3, yes, since
(2n^2 - 1) < 2n^2
(3n^5 + 2n + 1) > 3n^5
(2n^2 - 1) < 2n^2
(3n^5 + 2n + 1) > 3n^5