Solve 1/2+1/4+1/16+1/32+frac{1}{128}+frac{1}{256}=

$$\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 16 } + \frac { 1 } { 32 } + \frac { 1 } { 128 } + \frac { 1 } { 256 } =$$

Evaluate

$$\frac{219}{256}=0.85546875$$

Solution Steps

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

$$\frac{2}{4}+\frac{1}{4}+\frac{1}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{4}+\frac{1}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}+\frac{1}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Least common multiple of 4 and 16 is 16. Convert \frac{3}{4} and \frac{1}{16} to fractions with denominator 16.

$$\frac{12}{16}+\frac{1}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Since \frac{12}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{12+1}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Add 12 and 1 to get 13.

$$\frac{13}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Least common multiple of 16 and 32 is 32. Convert \frac{13}{16} and \frac{1}{32} to fractions with denominator 32.

$$\frac{26}{32}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}$$

Since \frac{26}{32} and \frac{1}{32} have the same denominator, add them by adding their numerators.

$$\frac{26+1}{32}+\frac{1}{128}+\frac{1}{256}$$

Add 26 and 1 to get 27.

$$\frac{27}{32}+\frac{1}{128}+\frac{1}{256}$$

Least common multiple of 32 and 128 is 128. Convert \frac{27}{32} and \frac{1}{128} to fractions with denominator 128.

$$\frac{108}{128}+\frac{1}{128}+\frac{1}{256}$$

Since \frac{108}{128} and \frac{1}{128} have the same denominator, add them by adding their numerators.

$$\frac{108+1}{128}+\frac{1}{256}$$

Add 108 and 1 to get 109.

$$\frac{109}{128}+\frac{1}{256}$$

Least common multiple of 128 and 256 is 256. Convert \frac{109}{128} and \frac{1}{256} to fractions with denominator 256.

$$\frac{218}{256}+\frac{1}{256}$$

Since \frac{218}{256} and \frac{1}{256} have the same denominator, add them by adding their numerators.

$$\frac{218+1}{256}$$

Add 218 and 1 to get 219.

$$\frac{219}{256}$$

Factor

$$\frac{3 \cdot 73}{2 ^ {8}} = 0.85546875$$