Solve 2+(-1)+1/2+(-1/4)+1/8+(-1/16)+frac{1}{32}+(-frac{1}{64})

$$2 + ( - 1 ) + \frac { 1 } { 2 } + ( - \frac { 1 } { 4 } ) + \frac { 1 } { 8 } + ( - \frac { 1 } { 16 } ) + \frac { 1 } { 32 } + ( - \frac { 1 } { 64 } )$$

Evaluate

$$\frac{85}{64}=1.328125$$

Solution Steps

Subtract 1 from 2 to get 1.

$$1+\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

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

$$\frac{2}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

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

$$\frac{2+1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{6}{4}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Least common multiple of 4 and 8 is 8. Convert \frac{5}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{10}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Since \frac{10}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Add 10 and 1 to get 11.

$$\frac{11}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Least common multiple of 8 and 16 is 16. Convert \frac{11}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{22}{16}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Since \frac{22}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-1}{16}+\frac{1}{32}-\frac{1}{64}$$

Subtract 1 from 22 to get 21.

$$\frac{21}{16}+\frac{1}{32}-\frac{1}{64}$$

Least common multiple of 16 and 32 is 32. Convert \frac{21}{16} and \frac{1}{32} to fractions with denominator 32.

$$\frac{42}{32}+\frac{1}{32}-\frac{1}{64}$$

Since \frac{42}{32} and \frac{1}{32} have the same denominator, add them by adding their numerators.

$$\frac{42+1}{32}-\frac{1}{64}$$

Add 42 and 1 to get 43.

$$\frac{43}{32}-\frac{1}{64}$$

Least common multiple of 32 and 64 is 64. Convert \frac{43}{32} and \frac{1}{64} to fractions with denominator 64.

$$\frac{86}{64}-\frac{1}{64}$$

Since \frac{86}{64} and \frac{1}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{86-1}{64}$$

Subtract 1 from 86 to get 85.

$$\frac{85}{64}$$

Factor

$$\frac{5 \cdot 17}{2 ^ {6}} = 1\frac{21}{64} = 1.328125$$