Solve +1/2^2+1/4/4^2+1/6^2+frac{1}{8^2}

$$+ \frac { 1 } { 2 ^ { 2 } } + \frac { \frac { 1 } { 4 } } { 4 ^ { 2 } } + \frac { 1 } { 6 ^ { 2 } } + \frac { 1 } { 8 ^ { 2 } }$$

Evaluate

$$\frac{89}{288}\approx 0.309027778$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{4}+\frac{\frac{1}{4}}{4^{2}}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{4}+\frac{\frac{1}{4}}{16}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Express \frac{\frac{1}{4}}{16} as a single fraction.

$$\frac{1}{4}+\frac{1}{4\times 16}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Multiply 4 and 16 to get 64.

$$\frac{1}{4}+\frac{1}{64}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Least common multiple of 4 and 64 is 64. Convert \frac{1}{4} and \frac{1}{64} to fractions with denominator 64.

$$\frac{16}{64}+\frac{1}{64}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Since \frac{16}{64} and \frac{1}{64} have the same denominator, add them by adding their numerators.

$$\frac{16+1}{64}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Add 16 and 1 to get 17.

$$\frac{17}{64}+\frac{1}{6^{2}}+\frac{1}{8^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{17}{64}+\frac{1}{36}+\frac{1}{8^{2}}$$

Least common multiple of 64 and 36 is 576. Convert \frac{17}{64} and \frac{1}{36} to fractions with denominator 576.

$$\frac{153}{576}+\frac{16}{576}+\frac{1}{8^{2}}$$

Since \frac{153}{576} and \frac{16}{576} have the same denominator, add them by adding their numerators.

$$\frac{153+16}{576}+\frac{1}{8^{2}}$$

Add 153 and 16 to get 169.

$$\frac{169}{576}+\frac{1}{8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{169}{576}+\frac{1}{64}$$

Least common multiple of 576 and 64 is 576. Convert \frac{169}{576} and \frac{1}{64} to fractions with denominator 576.

$$\frac{169}{576}+\frac{9}{576}$$

Since \frac{169}{576} and \frac{9}{576} have the same denominator, add them by adding their numerators.

$$\frac{169+9}{576}$$

Add 169 and 9 to get 178.

$$\frac{178}{576}$$

Reduce the fraction \frac{178}{576} to lowest terms by extracting and canceling out 2.

$$\frac{89}{288}$$

Factor

$$\frac{89}{2 ^ {5} \cdot 3 ^ {2}} = 0.3090277777777778$$