Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$

Abstract

We find various series that involves the central binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function ${}_p{F}_q$ approach, our method utilizes a straightforward transformation to obtain new evaluations linked to Fibonacci numbers and the golden ratio. Before the end of this paper, we also gave a new series representation for $\zeta (2)$.

9 pages