If (n + 1)! = 90 [(n − 1)!], find n.

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Solution

(n + 1)! = 90 [(n − 1)!]
$\Rightarrow$ (n + 1) $\times$ (n) $\times$ (n−1)! = 90[(n − 1)!]
$\Rightarrow$ (n + 1) $\times$ (n) = 90
$\Rightarrow$ (n + 1) $\times$ (n) = 10 $\times$ 9
On comparing, we get:
n = 9

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