Table 2 Numerical results of \(\pmb{a_{i}=L_{i}}\) , \(\pmb{r=1}\)

1

2

2

\(\frac{2}{2}=1\)

2

\(\sqrt{10}\)

\(\sqrt{10}\)

\(\frac{\sqrt{10}}{\sqrt{10}}=1\)

3

\(\sqrt{42}\)

\(\sqrt{154}\)

\(\frac{\sqrt{154}}{\sqrt {42}}\approx 1.915\)

4

\(\sqrt{120}\)

\(\sqrt{810}\)

\(\frac{\sqrt{810}}{\sqrt {120}}\approx 2.598\)

5

\(\sqrt{395}\)

\(\sqrt{6{,}004}\)

\(\frac{\sqrt{6{,}004}}{\sqrt {395}}\approx3.899\)

6

\(\sqrt{1{,}200}\)

\(\sqrt{39{,}400}\)

\(\frac{\sqrt{39{,}400}}{\sqrt {1{,}200}}\approx5.730\)

n

\(\sqrt{n^{-1}(5F_{n}F_{n-1}+1)}\)  n odd,

\(\sqrt{n^{-1}(5F_{n}F_{n-1}-3)}\)  n even