\[\begin{array}{l}
{\text{Докажите по индукции:}} \hfill \\
\sum\limits_{k = 1}^n {\frac{1}{{k\left( {k + 1} \right)\left( {k + 2} \right)}}} = \frac{{n\left( {n + 3} \right)}}{{4\left( {n + 1} \right)\left( {n + 2} \right)}}. \hfill \\
\end{array}\]