Solve f(x)=1+1/1^2+1/2^2+1/3^2

$$f ( x ) = 1 + \frac { 1 } { 1 ^ { 2 } } + \frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { 3 ^ { 2 } }$$

Evaluate

$$\frac{85}{36}\approx 2.361111111$$

Solution Steps

Rewrite 1^{2} as 1\times 1. Cancel out 1 in both numerator and denominator.

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

Divide 1 by 1 to get 1.

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

Add 1 and 1 to get 2.

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

Calculate 2 to the power of 2 and get 4.

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

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}+\frac{1}{4}+\frac{1}{3^{2}}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{4}+\frac{1}{3^{2}}$$

Add 8 and 1 to get 9.

$$\frac{9}{4}+\frac{1}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{4}+\frac{1}{9}$$

Least common multiple of 4 and 9 is 36. Convert \frac{9}{4} and \frac{1}{9} to fractions with denominator 36.

$$\frac{81}{36}+\frac{4}{36}$$

Since \frac{81}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$\frac{81+4}{36}$$

Add 81 and 4 to get 85.

$$\frac{85}{36}$$

Factor

$$\frac{5 \cdot 17}{2 ^ {2} \cdot 3 ^ {2}} = 2\frac{13}{36} = 2.361111111111111$$