Solve 2^-1+3^-1-4^-1+5^-1

$${ 2 }^{ -1 } + { 3 }^{ -1 } - { 4 }^{ -1 } + { 5 }^{ -1 }$$

Evaluate

$$\frac{47}{60}\approx 0.783333333$$

Solution Steps

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

$$\frac{1}{2}+3^{-1}-4^{-1}+5^{-1}$$

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

$$\frac{1}{2}+\frac{1}{3}-4^{-1}+5^{-1}$$

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$\frac{5}{6}-4^{-1}+5^{-1}$$

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

$$\frac{5}{6}-\frac{1}{4}+5^{-1}$$

Subtract \frac{1}{4} from \frac{5}{6} to get \frac{7}{12}.

$$\frac{7}{12}+5^{-1}$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{7}{12}+\frac{1}{5}$$

Add \frac{7}{12} and \frac{1}{5} to get \frac{47}{60}.

$$\frac{47}{60}$$

Factor

$$\frac{47}{2 ^ {2} \cdot 3 \cdot 5} = 0.7833333333333333$$