Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
\frac{{n! - (n - 1)!}}{{(n + 1)!}} = \frac{1}{6}(dk:n \ge 1;n \in N)\\
\Leftrightarrow \frac{{n!}}{{(n + 1)!}} - \frac{{(n - 1)!}}{{(n + 1)!}} = \frac{1}{6}\\
\Leftrightarrow \frac{1}{{n + 1}} - \frac{1}{{n(n + 1)}} = \frac{1}{6}\\
\Leftrightarrow n = 5 \to tm\\
\frac{{n!}}{{(n - 2)!}} - \frac{{n!}}{{(n - 1)!}} = 3(dk:n \ge 2;n \in N)\\
\Leftrightarrow n(n - 1) - n = 3\\
\Leftrightarrow \left[ \begin{array}{l}
n = 3 \to tm\\
n = - 1 \to loai
\end{array} \right.\\
{n^3} + \frac{{n!}}{{(n - 2)!}} = 10(dk:n \ge 2;n \in N)\\
\Leftrightarrow {n^3} + n(n - 1) = 10\\
\Leftrightarrow n = 2 \to tm
\end{array}\]
