Solve (5/2*3/5^{2})+(6/2*3/6^2)+(frac{7}{2}*frac{3}{7^2})+(frac{8}{2}*frac{3}{8^2})+(frac{9}{2}*frac{3}{9^2})

$$( \frac { 5 } { 2 } \cdot \frac { 3 } { 5 ^ { 2 } } ) + ( \frac { 6 } { 2 } \cdot \frac { 3 } { 6 ^ { 2 } } ) + ( \frac { 7 } { 2 } \cdot \frac { 3 } { 7 ^ { 2 } } ) + ( \frac { 8 } { 2 } \cdot \frac { 3 } { 8 ^ { 2 } } ) + ( \frac { 9 } { 2 } \cdot \frac { 3 } { 9 ^ { 2 } } )$$

Evaluate

$$\frac{1879}{1680}\approx 1.118452381$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{5}{2}\times \frac{3}{25}+\frac{6}{2}\times \frac{3}{6^{2}}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Multiply \frac{5}{2} times \frac{3}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{2\times 25}+\frac{6}{2}\times \frac{3}{6^{2}}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 25}.

$$\frac{15}{50}+\frac{6}{2}\times \frac{3}{6^{2}}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Reduce the fraction \frac{15}{50} to lowest terms by extracting and canceling out 5.

$$\frac{3}{10}+\frac{6}{2}\times \frac{3}{6^{2}}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Divide 6 by 2 to get 3.

$$\frac{3}{10}+3\times \frac{3}{6^{2}}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{3}{10}+3\times \frac{3}{36}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Reduce the fraction \frac{3}{36} to lowest terms by extracting and canceling out 3.

$$\frac{3}{10}+3\times \frac{1}{12}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Multiply 3 and \frac{1}{12} to get \frac{3}{12}.

$$\frac{3}{10}+\frac{3}{12}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{10}+\frac{1}{4}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Least common multiple of 10 and 4 is 20. Convert \frac{3}{10} and \frac{1}{4} to fractions with denominator 20.

$$\frac{6}{20}+\frac{5}{20}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Since \frac{6}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{6+5}{20}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Add 6 and 5 to get 11.

$$\frac{11}{20}+\frac{7}{2}\times \frac{3}{7^{2}}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{11}{20}+\frac{7}{2}\times \frac{3}{49}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Multiply \frac{7}{2} times \frac{3}{49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{20}+\frac{7\times 3}{2\times 49}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Do the multiplications in the fraction \frac{7\times 3}{2\times 49}.

$$\frac{11}{20}+\frac{21}{98}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Reduce the fraction \frac{21}{98} to lowest terms by extracting and canceling out 7.

$$\frac{11}{20}+\frac{3}{14}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Least common multiple of 20 and 14 is 140. Convert \frac{11}{20} and \frac{3}{14} to fractions with denominator 140.

$$\frac{77}{140}+\frac{30}{140}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Since \frac{77}{140} and \frac{30}{140} have the same denominator, add them by adding their numerators.

$$\frac{77+30}{140}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Add 77 and 30 to get 107.

$$\frac{107}{140}+\frac{8}{2}\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Divide 8 by 2 to get 4.

$$\frac{107}{140}+4\times \frac{3}{8^{2}}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{107}{140}+4\times \frac{3}{64}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Express 4\times \frac{3}{64} as a single fraction.

$$\frac{107}{140}+\frac{4\times 3}{64}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Multiply 4 and 3 to get 12.

$$\frac{107}{140}+\frac{12}{64}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Reduce the fraction \frac{12}{64} to lowest terms by extracting and canceling out 4.

$$\frac{107}{140}+\frac{3}{16}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Least common multiple of 140 and 16 is 560. Convert \frac{107}{140} and \frac{3}{16} to fractions with denominator 560.

$$\frac{428}{560}+\frac{105}{560}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Since \frac{428}{560} and \frac{105}{560} have the same denominator, add them by adding their numerators.

$$\frac{428+105}{560}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Add 428 and 105 to get 533.

$$\frac{533}{560}+\frac{9}{2}\times \frac{3}{9^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{533}{560}+\frac{9}{2}\times \frac{3}{81}$$

Reduce the fraction \frac{3}{81} to lowest terms by extracting and canceling out 3.

$$\frac{533}{560}+\frac{9}{2}\times \frac{1}{27}$$

Multiply \frac{9}{2} times \frac{1}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{533}{560}+\frac{9\times 1}{2\times 27}$$

Do the multiplications in the fraction \frac{9\times 1}{2\times 27}.

$$\frac{533}{560}+\frac{9}{54}$$

Reduce the fraction \frac{9}{54} to lowest terms by extracting and canceling out 9.

$$\frac{533}{560}+\frac{1}{6}$$

Least common multiple of 560 and 6 is 1680. Convert \frac{533}{560} and \frac{1}{6} to fractions with denominator 1680.

$$\frac{1599}{1680}+\frac{280}{1680}$$

Since \frac{1599}{1680} and \frac{280}{1680} have the same denominator, add them by adding their numerators.

$$\frac{1599+280}{1680}$$

Add 1599 and 280 to get 1879.

$$\frac{1879}{1680}$$

Factor

$$\frac{1879}{2 ^ {4} \cdot 3 \cdot 5 \cdot 7} = 1\frac{199}{1680} = 1.118452380952381$$