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Question
Find the value of n if (n + 1)! = 20(n − 1)!
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Solution
(n + 1)! = 20(n – 1)!
(n + 1) n(n – 1)! = 20(n – 1)!
n(n + 1) = 20
n2 + n – 20 = 0
n2 + 5n – 4n – 20 = 0
n(n + 5) – 4(n + 5) = 0
(n – 4)(n + 5) = 0
n – 4 = 0 or n + 5 = 0
n = 4 or n = – 5
But n = – 5 is not possible.
∴ n = 4
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