section_heading: Dokaz
paragraph_text: Oduzimanjem ove dvije jednadžbe slijedi <math> \alpha^n - \beta^n = F_n(\alpha - \beta), </math> a kako je <math> \alpha - \beta = \frac{1 + \sqrt{5}}{2} - \frac{1 - \sqrt{5}}{2} = \sqrt{5}, </math> konačno dobivamo <math> F_n = \frac{1}{\sqrt{5}}({\alpha}^n - {\beta}^n). </math><ref>https://artofproblemsolving.com/wiki/index.php/Binet%27s_Formula