If only it was (n-1)(n+1)

The Fibonacci sequence is given by F1=1 F_1 = 1, F2=1F_2 = 1 and Fn+1=Fn+Fn1 F_{n+1} = F_n + F_{n-1} . What is

n=21Fn1Fn+1? \sum_{n=2}^\infty \frac{ 1 } { F_{n-1} F_{n+1} } ?

Give your answer to 2 decimal places.

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