Q. 74.1( 10 Votes )

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

Answer :

Given Equation :

(n + 1)! = 12 × (n - 1)!

To Find : Value of n

Formula :

By given equation,

(n + 1)! = 12 × (n - 1)!

By using above formula we can write,

∴(n + 1) × (n) × (n - 1)! = 12 × (n - 1)!

Cancelling the term (n - 1)! from both the sides,

∴(n + 1) × (n) = 12 …….. eq(1)

∴(n + 1) × (n) = (4) × (3)

Comparing both the sides, we get,

∴n = 3

Conclusion : Value of n is 3.

Note : Instead of taking product of two brackets in eq(1), it is easy to convert the constant term that is 12 into product of two __consecutive__ numbers and then by observing two sides of equation we can get value of n.

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