\[\begin{array}{l} {\text{Докажите}}{\text{, что}} \hfill \\ {\left( {\frac{a}{{a - 1}}} \right)^{\frac{{b - 1}}{b}}} = 1 + \frac{{1 + \frac{{1 + \frac{{...}}{{{a_3}}}}}{{{a_2}}}}}{{{a_1}}}, \hfill \\ {\text{где }}{a_k} = a + \frac{a}{{b \cdot k - 1}},{\text{ }}a,b > 1. \hfill \\ \end{array} \]