Find n, if : 1 n ! =1 4 ! -4 5 ! - Vidyadip

Question

Find n, if : $\frac{1}{n !}=\frac{1}{4 !}-\frac{4}{5 !}$

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Answer

$
\begin{array}{ll}
& \frac{1}{n !}=\frac{1}{4 !}-\frac{4}{5 !} \\
\therefore & \frac{1}{n !}=\frac{1}{4 !}-\frac{4}{5 !} \\
\therefore & \frac{1}{n !}=\frac{5}{5 \times 4 !}-\frac{4}{5 !} \\
\therefore & \frac{1}{n !}=\frac{5}{5 !}-\frac{4}{5 !} \\
\therefore & \frac{1}{n !}=\frac{1}{5 !} \\
\therefore & n !=5 ! \\
\therefore & n=5
\end{array}
$

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