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

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Solution

Simplify the right hand side of $n! (n + 2) = n! + (n + 1)!$ .

$n! + (n + 1)!$

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

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

$= n! (n + 2)$

$= L H S$
Hence LHS=RHS

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