\[\begin{array}{l} {\text{Вычислить:}} \hfill \\ \frac{1}{{\frac{1}{{101}} + \frac{1}{{\frac{1}{{100}} + \frac{1}{{\frac{1}{{99}} + ... + \frac{1}{{\frac{1}{3} + \frac{1}{{\frac{1}{2} + 1}}}}}}}}}}. \hfill \\ \end{array}\]