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Find sum_{n=3}^{\infty}(18+999F_n/(F_{n-1}X F_{n+1})

Source: MTRP 2018 Class 11-Multiple Choice Question: Problem 3 :-

February 17, 2021
Fibonaccialgebra

Problem Statement

FnF_{n} denotes the Fibonacci Sequence where F1=0,F2=1,Fn=Fn−1+Fn−2, ∀ n≥3F_{1}=0, F_{2}=1, F_{n}=F_{n-1}+F_{n-2},\ \forall \ n \geq 3 Find∑n=3∞18+999FnFn−1×Fn+1\sum\limits_{n=3}^{\infty}\frac{18+999F_n}{F_{n-1}\times F_{n+1}}
[*] 2016 [*] 2017 [*] 2018 [*] None of these
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