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

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

Evaluate

$$\frac{35}{48}\approx 0.729166667$$

Solution Steps

Divide 1 by 1 to get 1.

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

Divide 1 by 1 to get 1.

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

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

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

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{1}{16}+\left(1+\frac{1}{2}\right)^{-1}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{1}{16}+\left(\frac{3}{2}\right)^{-1}$$

Calculate \frac{3}{2} to the power of -1 and get \frac{2}{3}.

$$\frac{1}{16}+\frac{2}{3}$$

Add \frac{1}{16} and \frac{2}{3} to get \frac{35}{48}.

$$\frac{35}{48}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {4} \cdot 3} = 0.7291666666666666$$