On some series involving the binomial coefficients $\left(\genfrac{}{}{0ex}{}{3n}{n}\right)$

Abstract

Using a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $\left(\genfrac{}{}{0ex}{}{3n}{n}\right)$ derived by Necdet Batir. New evaluations are given; and connections with Fibonacci numbers and the golden ratio are established. Finally, we derive some Fibonacci and Lucas series involving the reciprocals of $\left(\genfrac{}{}{0ex}{}{3n}{n}\right)$.

17 pages