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If (n + 1)! = 12 × [(n – 1)!], find the value of n.

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To Find: Value of n 

Given: (n+1)! = 12× [(n-1)!] 

Formula Used: n! = (n) × (n-1) × (n-2) × (n-3) ………. 3 × 2 × 1

Now, (n+1)! = 12× [(n-1)!] 

⇒ (n+1) × (n) × [(n-1)!] = 12 × [(n-1)!] 

⇒ (n+1) × (n) = 12 

⇒ n2+n = 12

 ⇒ n2+n-12 = 0 

⇒ (n-3) (n+4) = 0 

⇒ n = 3 or, n = -4 

But, n=-4 is not possible because in case of factorial (!) n cannot be negative. Hence, n=3 is the correct answer.

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