Inequalities and completely monotonic functions associated with the ratios of functions resulting from the gamma function

We prove that some functions associated with the products ∏k=1n2k-12k, ∏k=1n3k-23k-1,∏k=1n3k-23k and ∏k=1n3k-13k are completely monotonic. By using the results obtained, we derive some inequalities for the previous products. Our results improve some known inequalities.