Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients C(2n,n)

We find various series that involve the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward transformation to obtain new evaluations linked to Fibonacci numbers and the golden ratio. We also gave a new series representation for $\zeta(2)$.