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

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

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

expand

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

\frac{n ^{2}}{2} + \frac{3 n}{2} + 1

Solution steps

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

Expand

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

= \frac{n ^{2} + 3 n + 2}{2}

Apply the fraction rule:

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

\frac{n ^{2} + 3 n + 2}{2} = \frac{n ^{2}}{2} + \frac{3 n}{2} + \frac{2}{2}

= \frac{n ^{2}}{2} + \frac{3 n}{2} + \frac{2}{2}

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

= \frac{n ^{2}}{2} + \frac{3 n}{2} + 1

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