Solve 1/4+2+1/4+2^2+1/1+2^3

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

Evaluate

$$\frac{29}{72}\approx 0.402777778$$

Solution Steps

Add 4 and 2 to get 6.

$$\frac{1}{6}+\frac{1}{4+2^{2}}+\frac{1}{1+2^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{6}+\frac{1}{4+4}+\frac{1}{1+2^{3}}$$

Add 4 and 4 to get 8.

$$\frac{1}{6}+\frac{1}{8}+\frac{1}{1+2^{3}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{1}{8} to fractions with denominator 24.

$$\frac{4}{24}+\frac{3}{24}+\frac{1}{1+2^{3}}$$

Since \frac{4}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{24}+\frac{1}{1+2^{3}}$$

Add 4 and 3 to get 7.

$$\frac{7}{24}+\frac{1}{1+2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{7}{24}+\frac{1}{1+8}$$

Add 1 and 8 to get 9.

$$\frac{7}{24}+\frac{1}{9}$$

Least common multiple of 24 and 9 is 72. Convert \frac{7}{24} and \frac{1}{9} to fractions with denominator 72.

$$\frac{21}{72}+\frac{8}{72}$$

Since \frac{21}{72} and \frac{8}{72} have the same denominator, add them by adding their numerators.

$$\frac{21+8}{72}$$

Add 21 and 8 to get 29.

$$\frac{29}{72}$$

Factor

$$\frac{29}{2 ^ {3} \cdot 3 ^ {2}} = 0.4027777777777778$$