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Question
Find n, if (n + 1)! = 42 × (n – 1)!
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Solution
(n + 1)! = 42 × (n – 1)!
∴ (n + 1) n (n – 1)! = 42(n – 1)!
∴ n2 + n = 42
∴ n2 + n – 42 = 0
∴ (n + 7)(n – 6) = 0
∴ n = – 7 or n = 6
But n ≠ – 7 as n ∈ N
∴ n = 6
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