Recurrence Relations and Inequalities

First, we present a procedure that is capable of proving many inequalities involving recursively defined sequences automatically. Second, we take a closer look at the positivity of C-finite sequences. We give proofs that certain C-finite sequences have infinitely many sign changes. For this purpose we appeal to classical theorems that are not obviously related to this kind of problem, such as Minkowski's theorem and the Kronecker-Weyl theorem.