Solve 1/13+1/3!*13+1/5!*21+1/7*29

$$\frac { 1 } { 13 } + \frac { 1 } { 3 ! \cdot 13 } + \frac { 1 } { 5 ! \cdot 21 } + \frac { 1 } { 7 \cdot 29 }$$

Evaluate

$$\frac{90317}{950040}\approx 0.095066524$$

Solution Steps

The factorial of 3 is 6.

$$\frac{1}{13}+\frac{1}{6\times 13}+\frac{1}{5!\times 21}+\frac{1}{7\times 29}$$

Multiply 6 and 13 to get 78.

$$\frac{1}{13}+\frac{1}{78}+\frac{1}{5!\times 21}+\frac{1}{7\times 29}$$

Least common multiple of 13 and 78 is 78. Convert \frac{1}{13} and \frac{1}{78} to fractions with denominator 78.

$$\frac{6}{78}+\frac{1}{78}+\frac{1}{5!\times 21}+\frac{1}{7\times 29}$$

Since \frac{6}{78} and \frac{1}{78} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{78}+\frac{1}{5!\times 21}+\frac{1}{7\times 29}$$

Add 6 and 1 to get 7.

$$\frac{7}{78}+\frac{1}{5!\times 21}+\frac{1}{7\times 29}$$

The factorial of 5 is 120.

$$\frac{7}{78}+\frac{1}{120\times 21}+\frac{1}{7\times 29}$$

Multiply 120 and 21 to get 2520.

$$\frac{7}{78}+\frac{1}{2520}+\frac{1}{7\times 29}$$

Least common multiple of 78 and 2520 is 32760. Convert \frac{7}{78} and \frac{1}{2520} to fractions with denominator 32760.

$$\frac{2940}{32760}+\frac{13}{32760}+\frac{1}{7\times 29}$$

Since \frac{2940}{32760} and \frac{13}{32760} have the same denominator, add them by adding their numerators.

$$\frac{2940+13}{32760}+\frac{1}{7\times 29}$$

Add 2940 and 13 to get 2953.

$$\frac{2953}{32760}+\frac{1}{7\times 29}$$

Multiply 7 and 29 to get 203.

$$\frac{2953}{32760}+\frac{1}{203}$$

Least common multiple of 32760 and 203 is 950040. Convert \frac{2953}{32760} and \frac{1}{203} to fractions with denominator 950040.

$$\frac{85637}{950040}+\frac{4680}{950040}$$

Since \frac{85637}{950040} and \frac{4680}{950040} have the same denominator, add them by adding their numerators.

$$\frac{85637+4680}{950040}$$

Add 85637 and 4680 to get 90317.

$$\frac{90317}{950040}$$

Factor

$$\frac{37 \cdot 2441}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7 \cdot 13 \cdot 29} = 0.09506652351479938$$