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

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

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expand ((k+1)(k+2))/2

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

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

(5 + 3) (5 - 2) (5 + 1)

(x + y) (x - y)

(x - π)^{2}

(e^{i z} - e^{- i z})^{2}

(e^{- t} + e^{2 t})^{2}

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