Solve =1-(1/2)^5/1-frac{1{2}}

$$= \frac { 1 - ( \frac { 1 } { 2 } ) ^ { 5 } } { 1 - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{31}{16}=1.9375$$

Solution Steps

Calculate \frac{1}{2} to the power of 5 and get \frac{1}{32}.

$$\frac{1-\frac{1}{32}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{32}{32}.

$$\frac{\frac{32}{32}-\frac{1}{32}}{1-\frac{1}{2}}$$

Since \frac{32}{32} and \frac{1}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{32-1}{32}}{1-\frac{1}{2}}$$

Subtract 1 from 32 to get 31.

$$\frac{\frac{31}{32}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{31}{32}}{\frac{2}{2}-\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{31}{32}}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{31}{32}}{\frac{1}{2}}$$

Divide \frac{31}{32} by \frac{1}{2} by multiplying \frac{31}{32} by the reciprocal of \frac{1}{2}.

$$\frac{31}{32}\times 2$$

Express \frac{31}{32}\times 2 as a single fraction.

$$\frac{31\times 2}{32}$$

Multiply 31 and 2 to get 62.

$$\frac{62}{32}$$

Reduce the fraction \frac{62}{32} to lowest terms by extracting and canceling out 2.

$$\frac{31}{16}$$

Factor

$$\frac{31}{2 ^ {4}} = 1\frac{15}{16} = 1.9375$$