n | Theorem 2.1 | Theorem 1.3 | \(\frac{\mathbf{Third\ column}}{\mathbf{Second\ column}}\) |
---|---|---|---|
2 | 1 | 1 | \(\frac{1}{1}=1\) |
3 | 2 | 2 | \(\frac{2}{2}=1\) |
4 | \(3\sqrt{2}\) | 6 | \(\frac{6}{3\sqrt{2}}=\sqrt{2}\) |
5 | \(\sqrt{60}\) | 15 | \(\frac{15}{\sqrt{60}}\approx1.936\) |
6 | \(\sqrt{200}\) | 40 | \(\frac{40}{\sqrt{200}}=2\sqrt{2}\) |
n | \(\sqrt{(n-1)F_{n}F_{n-1}}\) | \(F_{n}F_{n-1}\) | \(\frac {F_{n}F_{n-1}}{\sqrt{(n-1)F_{n}F_{n-1}}}=\sqrt{\frac {F_{n}F_{n-1}}{n-1}}\) |