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

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

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simplify (k(k+1)+2(k+1))/2

simplify

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

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

Solution steps

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

Expand

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

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

Expand

2 (k + 1) : 2 k + 2

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

Add similar elements:

k + 2 k = 3 k

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

\frac{1}{( - 1 )}

2 m^{2} - 8 m

(- 8)^{1}

(- 3) (6)

\frac{9 !}{3 ! \cdot 6 !}