On Some Series Involving the Central Binomial Coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy

TL;DR
This paper investigates series involving central binomial coefficients, deriving new closed-form formulas, analyzing convergence, and establishing identities with Fibonacci and Lucas numbers.
Contribution
It introduces novel series representations and identities involving central binomial coefficients, including those with alternating signs and connections to Fibonacci and Lucas numbers.
Findings
Derived new closed-form series representations
Analyzed convergence properties of alternating series
Established identities linking binomial coefficients with Fibonacci and Lucas numbers
Abstract
In this paper, we explore a variety of series involving the central binomial coefficients, highlighting their structural properties and connections to other mathematical objects. Specifically, we derive new closed-form representations and examine the convergence properties of infinite series with a repeating alternation pattern of signs involving central binomial coefficients. More concretely, we derive the series where represents both and . Also, we present novel series involving Fibonacci and Lucas numbers, deriving many interesting identities.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Mathematical Theories and Applications · Advanced Combinatorial Mathematics
