Question:
If $(n+1) !=12 \times(n-1) !$, find the value of $n$.
Solution:
Given Equation :
$(n+1) !=12 \times(n-1) !$
To Find : Value of n
Formula: $n !=n \times(n-1) !$
By given equation,
$(n+1) !=12 \times(n-1) !$
By using above formula we can write,
$\therefore(n+1) \times(n) \times(n-1) !=12 \times(n-1) !$
Cancelling the term $(n-1) !$ from both the sides,
$\therefore(n+1) \times(n)=12 \ldots \ldots \ldots$ eq(1)
$\therefore(n+1) \times(n)=(4) \times(3)$
Comparing both the sides, we get,
$\therefore \mathrm{n}=3$
Conclusion : Value of n is 3.
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