Explicit Identities and new results for Infinite Series associated with the Ratio of Central Binomial Coefficients

We investigate some classes of infinite series involving central binomial coefficients, particularly focusing on those arising from ratios such as $\left(\genfrac{}{}{0px}{}{2n}{n}\right){\left(\genfrac{}{}{0px}{}{4n}{2n}\right)}^{-1}$,$\left(\genfrac{}{}{0px}{}{4n}{2n}\right){\left(\genfrac{}{}{0px}{}{2n}{n}\right)}^{-1}$ and related expressions. We derive several new explicit identities and closed-form evaluations, building on and refining previous results by Bhandari (2022) and Adegoke et al. (2022).