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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