Discovering and proving upper and lower bound for sequences to support inequality proofs

We propose to give upper and lower bounds in terms of known functions of certain sequences in n defined as sums. The final goal of these estimations is to prove inequalities involving these sequences. For example log concavity of such sequences and higher order Turan inequalities. The idea of the project is to make numerical […]

We propose to give upper and lower bounds in terms of known functions of certain sequences in n defined as sums. The final goal of these estimations is to prove inequalities involving these sequences. For example log concavity of such sequences and higher order Turan inequalities. The idea of the project is to make numerical experiments using computer algebra and from the data obtained proposing a conjecture and then proving it by using mathematical induction.