Solve =k(k+1)+2(k+1)/2

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

Evaluate

$$\frac{\left(k+1\right)\left(k+2\right)}{2}$$

Solution Steps

Use the distributive property to multiply k by k+1.

$$\frac{k^{2}+k+2\left(k+1\right)}{2}$$

Use the distributive property to multiply 2 by k+1.

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

Combine k and 2k to get 3k.

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

Expand

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

Solution Steps

Use the distributive property to multiply k by k+1.

$$\frac{k^{2}+k+2\left(k+1\right)}{2}$$

Use the distributive property to multiply 2 by k+1.

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

Combine k and 2k to get 3k.

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