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Table 1 Some values of \((\sum^{\infty}_{k=n}\frac{1}{f_{k}^{2}})^{-1}\)

From: Asymptotic behavior of reciprocal sum of two products of Fibonacci numbers

n

\((\sum^{\infty}_{k=n}\frac{1}{f_{k}^{2}} )^{-1}\)

\(f_{n}^{2}-f_{n-1}^{2}\)

n

\((\sum^{\infty}_{k=n}\frac{1}{f_{k}^{2}} )^{-1}\)

\(f_{n}^{2}-f_{n-1}^{2}\)

3

2.3456…

3

4

5.6714…

5

5

15.3351…

16

6

39.6673…

39

7

104.3335…

105

8

272.6667…

272

9

714.3333…

715

10

1869.6666…

1869