Σ_(n=0) ^∞ ((((√5)−2)^n (((2n)),(n) ))/(((2n+1)(((√5)+(1/( (√5))))^(n+(1/2)) +((√5)−(1/( (√5))))^(n−(1/2)) ))))


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Question Number 125884 by Dwaipayan Shikari last updated on 14/Dec/20

$\underset{n = 0}{\sum^{\infty}} \frac{{(\sqrt{5} - 2)}^{n} (\begin{matrix} 2 n \\ n \end{matrix})}{((2 n + 1) ({(\sqrt{5} + \frac{1}{\sqrt{5}})}^{n + \frac{1}{2}} + {(\sqrt{5} - \frac{1}{\sqrt{5}})}^{n - \frac{1}{2}}))}$
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