\[\begin{array}{l}
{\text{Вычислите:}} \hfill \\
\frac{1}{{1 \cdot 2}} + \frac{1}{{2 \cdot 3}} + \frac{1}{{3 \cdot 4}} + ... + \frac{1}{{99 \cdot 100}}. \hfill \\
\end{array}\]
\[\frac{1}{{k \cdot \left( {k + 1} \right)}} = \frac{1}{k} - \frac{1}{{k + 1}}\]
\[\frac{{99}}{{100}}\]
