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If $(n+1) !=12 \times(n-1) !$, find the value of $n$.



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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