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

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Solution

LHS = n! (n+2) = n! + (n+1)!
= n! (n+1)! = n! + (n+1)(n+1-1)!
= n! + (n+1)! = n! + (1+n+1) = n! (n+2)
=LHS
$∴$ n! (n+2) = n! + (n+1)!
Hence, proved.

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