How do you simplify $((n+2)! )/( n!)$ ?

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Answer 1 · 2018-03-02T15:11:43

$n^2+3n+2$

We can rewrite the numerator as:

$((n+2) * (n+2-1) * (n+2-2)!)/((n)!)$

$=((n+2) * (n+1) * (n)!)/((n)!)$

We can cancel $(n)!$ and $(n)!$ out:

$=((n+2) * (n+1) * 1)/1$

$=(n+2) * (n+1)$

$=n^2+3n+2$

Thus, solved

How do you simplify ((n+2)! )/( n!)((n+2)! )/( n!)?