Solve 1/2+1/4+1/8+1/16+frac{1}{32}=

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

Evaluate

$$\frac{31}{32}=0.96875$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{6}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$$

Since \frac{6}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{8}+\frac{1}{16}+\frac{1}{32}$$

Add 6 and 1 to get 7.

$$\frac{7}{8}+\frac{1}{16}+\frac{1}{32}$$

Least common multiple of 8 and 16 is 16. Convert \frac{7}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{14}{16}+\frac{1}{16}+\frac{1}{32}$$

Since \frac{14}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{14+1}{16}+\frac{1}{32}$$

Add 14 and 1 to get 15.

$$\frac{15}{16}+\frac{1}{32}$$

Least common multiple of 16 and 32 is 32. Convert \frac{15}{16} and \frac{1}{32} to fractions with denominator 32.

$$\frac{30}{32}+\frac{1}{32}$$

Since \frac{30}{32} and \frac{1}{32} have the same denominator, add them by adding their numerators.

$$\frac{30+1}{32}$$

Add 30 and 1 to get 31.

$$\frac{31}{32}$$

Factor

$$\frac{31}{2 ^ {5}} = 0.96875$$