What is expand ((n+1)(n+2))/((n+2)!) ?

The solution to expand ((n+1)(n+2))/((n+2)!) is (n^2)/((n+2)!)+(3n)/((n+2)!)+2/((n+2)!)

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expand ((n+1)(n+2))/((n+2)!)

expand

\frac{( n + 1 ) ( n + 2 )}{( n + 2 ) !}

\frac{n ^{2}}{( n + 2 ) !} + \frac{3 n}{( n + 2 ) !} + \frac{2}{( n + 2 ) !}

Solution steps

\frac{( n + 1 ) ( n + 2 )}{( n + 2 ) !}

Expand

(n + 1) (n + 2) : n^{2} + 3 n + 2

= \frac{n ^{2} + 3 n + 2}{( n + 2 ) !}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{n ^{2} + 3 n + 2}{( n + 2 ) !} = \frac{n ^{2}}{( n + 2 ) !} + \frac{3 n}{( n + 2 ) !} + \frac{2}{( n + 2 ) !}

= \frac{n ^{2}}{( n + 2 ) !} + \frac{3 n}{( n + 2 ) !} + \frac{2}{( n + 2 ) !}

\frac{- 10 ( x + 3 ) ^{\frac{3}{2}} + 2 ( x + 3 ) ^{\frac{5}{2}}}{5}

\frac{1}{2} (- 2 x + 2) + 2

\frac{500 k}{( s ^{2} + 25 s + 100 k ) ( s ^{2} + 1 )}

7 (5 + 11)

- \frac{4 x}{5 ( x ^{2} + y )}

What is expand ((n+1)(n+2))/((n+2)!) ?
The solution to expand ((n+1)(n+2))/((n+2)!) is (n^2)/((n+2)!)+(3n)/((n+2)!)+2/((n+2)!)