Solve 1+1/3+1/10+1/42+1/216+frac{1}{1440}+frac{1}{9360}

$$1 + \frac { 1 } { 3 } + \frac { 1 } { 10 } + \frac { 1 } { 42 } + \frac { 1 } { 216 } + \frac { 1 } { 1440 } + \frac { 1 } { 9360 }$$

Evaluate

$$\frac{574967}{393120}\approx 1.462573769$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}+\frac{1}{3}+\frac{1}{10}+\frac{1}{42}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{3}+\frac{1}{10}+\frac{1}{42}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Add 3 and 1 to get 4.

$$\frac{4}{3}+\frac{1}{10}+\frac{1}{42}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Least common multiple of 3 and 10 is 30. Convert \frac{4}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{40}{30}+\frac{3}{30}+\frac{1}{42}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Since \frac{40}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{40+3}{30}+\frac{1}{42}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Add 40 and 3 to get 43.

$$\frac{43}{30}+\frac{1}{42}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Least common multiple of 30 and 42 is 210. Convert \frac{43}{30} and \frac{1}{42} to fractions with denominator 210.

$$\frac{301}{210}+\frac{5}{210}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Since \frac{301}{210} and \frac{5}{210} have the same denominator, add them by adding their numerators.

$$\frac{301+5}{210}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Add 301 and 5 to get 306.

$$\frac{306}{210}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Reduce the fraction \frac{306}{210} to lowest terms by extracting and canceling out 6.

$$\frac{51}{35}+\frac{1}{216}+\frac{1}{1440}+\frac{1}{9360}$$

Least common multiple of 35 and 216 is 7560. Convert \frac{51}{35} and \frac{1}{216} to fractions with denominator 7560.

$$\frac{11016}{7560}+\frac{35}{7560}+\frac{1}{1440}+\frac{1}{9360}$$

Since \frac{11016}{7560} and \frac{35}{7560} have the same denominator, add them by adding their numerators.

$$\frac{11016+35}{7560}+\frac{1}{1440}+\frac{1}{9360}$$

Add 11016 and 35 to get 11051.

$$\frac{11051}{7560}+\frac{1}{1440}+\frac{1}{9360}$$

Least common multiple of 7560 and 1440 is 30240. Convert \frac{11051}{7560} and \frac{1}{1440} to fractions with denominator 30240.

$$\frac{44204}{30240}+\frac{21}{30240}+\frac{1}{9360}$$

Since \frac{44204}{30240} and \frac{21}{30240} have the same denominator, add them by adding their numerators.

$$\frac{44204+21}{30240}+\frac{1}{9360}$$

Add 44204 and 21 to get 44225.

$$\frac{44225}{30240}+\frac{1}{9360}$$

Reduce the fraction \frac{44225}{30240} to lowest terms by extracting and canceling out 5.

$$\frac{8845}{6048}+\frac{1}{9360}$$

Least common multiple of 6048 and 9360 is 393120. Convert \frac{8845}{6048} and \frac{1}{9360} to fractions with denominator 393120.

$$\frac{574925}{393120}+\frac{42}{393120}$$

Since \frac{574925}{393120} and \frac{42}{393120} have the same denominator, add them by adding their numerators.

$$\frac{574925+42}{393120}$$

Add 574925 and 42 to get 574967.

$$\frac{574967}{393120}$$

Factor

$$\frac{574967}{2 ^ {5} \cdot 3 ^ {3} \cdot 5 \cdot 7 \cdot 13} = 1\frac{181847}{393120} = 1.4625737688237688$$