giải phương trình x! – (x-1)! / (n+1)! =1/6 n!/(n-2)! -n!(n-1)! =3 n^3 +n!/(n-2)!=10

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giải phương trình
x! – (x-1)! / (n+1)! =1/6
n!/(n-2)! -n!(n-1)! =3
n^3 +n!/(n-2)!=10

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Caroline 10 phút 2021-09-16T17:54:18+00:00 1 Answers 0 views 0

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    0
    2021-09-16T17:55:30+00:00

    Đáp án:

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

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