Solve 1/2(n+1)(n+2)

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

Evaluate

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

Solution Steps

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

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

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

$$\frac{1}{2}nn+\frac{1}{2}n\times 2+\frac{1}{2}n+\frac{1}{2}\times 2$$

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

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

Cancel out 2 and 2.

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

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

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

Cancel out 2 and 2.

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

Expand

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

Solution Steps

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

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

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

$$\frac{1}{2}nn+\frac{1}{2}n\times 2+\frac{1}{2}n+\frac{1}{2}\times 2$$

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

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

Cancel out 2 and 2.

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

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

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

Cancel out 2 and 2.

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