Solve {left(1/2right)}^3+{left(1/2right)}^2+1/2

$${ \left( \frac{ 1 }{ 2 } \right) }^{ 3 } + { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } + \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{7}{8}=0.875$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{1}{8}+\left(\frac{1}{2}\right)^{2}+\frac{1}{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{8}+\frac{1}{4}+\frac{1}{2}$$

Least common multiple of 8 and 4 is 8. Convert \frac{1}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{1}{8}+\frac{2}{8}+\frac{1}{2}$$

Since \frac{1}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{8}+\frac{1}{2}$$

Add 1 and 2 to get 3.

$$\frac{3}{8}+\frac{1}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{3}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{3}{8}+\frac{4}{8}$$

Since \frac{3}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{8}$$

Add 3 and 4 to get 7.

$$\frac{7}{8}$$

Factor

$$\frac{7}{2 ^ {3}} = 0.875$$