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

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

Evaluate

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

Solution Steps

Add 1 and 1 to get 2.

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

Use the distributive property to multiply \frac{1}{2} by k+1.

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

Apply the distributive property by multiplying each term of \frac{1}{2}k+\frac{1}{2} by each term of k+2.

$$\frac{1}{2}kk+\frac{1}{2}k\times 2+\frac{1}{2}k+\frac{1}{2}\times 2$$

Multiply k and k to get k^{2}.

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

Cancel out 2 and 2.

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

Combine k and \frac{1}{2}k to get \frac{3}{2}k.

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

Cancel out 2 and 2.

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

Expand

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

Solution Steps

Add 1 and 1 to get 2.

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

Use the distributive property to multiply \frac{1}{2} by k+1.

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

Apply the distributive property by multiplying each term of \frac{1}{2}k+\frac{1}{2} by each term of k+2.

$$\frac{1}{2}kk+\frac{1}{2}k\times 2+\frac{1}{2}k+\frac{1}{2}\times 2$$

Multiply k and k to get k^{2}.

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

Cancel out 2 and 2.

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

Combine k and \frac{1}{2}k to get \frac{3}{2}k.

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

Cancel out 2 and 2.

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