Factorials - Prove that n!(n + 2) = n! + (n + 1)!

Question:

Prove that n!(n + 2)! = n! + (n + 1)!

Solution:

RHS

n! + (n + 1)!

= n! + (n + 1)(n + 1 - 1)!

Using the property n! = n x (n - 1)!

= n! + (n + 1)(n!)

= n! (1 + n + 1)

= n! (n + 2)

= LHS

Answer:

n!(n + 2) = n! + (n + 1)! since LHS = RHS

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