Solve 1/2+1/2^2+1/(-2)^3+1/(-2)^4

$$\frac { 1 } { 2 } + \frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { ( - 2 ) ^ { 3 } } + \frac { 1 } { ( - 2 ) ^ { 4 } }$$

Evaluate

$$\frac{11}{16}=0.6875$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{2}+\frac{1}{4}+\frac{1}{\left(-2\right)^{3}}+\frac{1}{\left(-2\right)^{4}}$$

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

$$\frac{2}{4}+\frac{1}{4}+\frac{1}{\left(-2\right)^{3}}+\frac{1}{\left(-2\right)^{4}}$$

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

$$\frac{2+1}{4}+\frac{1}{\left(-2\right)^{3}}+\frac{1}{\left(-2\right)^{4}}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}+\frac{1}{\left(-2\right)^{3}}+\frac{1}{\left(-2\right)^{4}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{3}{4}+\frac{1}{-8}+\frac{1}{\left(-2\right)^{4}}$$

Fraction \frac{1}{-8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$\frac{3}{4}-\frac{1}{8}+\frac{1}{\left(-2\right)^{4}}$$

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

$$\frac{6}{8}-\frac{1}{8}+\frac{1}{\left(-2\right)^{4}}$$

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

$$\frac{6-1}{8}+\frac{1}{\left(-2\right)^{4}}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{8}+\frac{1}{\left(-2\right)^{4}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{5}{8}+\frac{1}{16}$$

Least common multiple of 8 and 16 is 16. Convert \frac{5}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{10}{16}+\frac{1}{16}$$

Since \frac{10}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{16}$$

Add 10 and 1 to get 11.

$$\frac{11}{16}$$

Factor

$$\frac{11}{2 ^ {4}} = 0.6875$$