Factorials - If (n + 2)! = 2550 (n!), find n?
Question:
If (n + 2)! = 2550 (n!), find n?
Solution:
(n + 2)! = 2550 (n!)
∴ (n + 2)! / (n!) = 2550
∴ [(n + 2) (n + 1) n!] / n! = 2550
∴ [(n + 2) (n + 1) ̶n̶!̶] / ̶n̶!̶ = 2550
∴ [(n + 2) (n + 1)] / = 2550
∴ [(n + 2) (n + 1)] / = 51 x 50
∴ By comparison
n + 2 = 51
∴ n = 49
Answer:
If (n + 2)! = 2550 (n!), n = 49.
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