Solve 1+1+1/2+1/6+1/24+1/120

$$1 + 1 + \frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 24 } + \frac { 1 } { 120 }$$

Evaluate

$$\frac{163}{60}\approx 2.716666667$$

Solution Steps

Add 1 and 1 to get 2.

$$2+\frac{1}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}$$

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

$$\frac{4}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}$$

Add 4 and 1 to get 5.

$$\frac{5}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}$$

Least common multiple of 2 and 6 is 6. Convert \frac{5}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{15}{6}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}$$

Since \frac{15}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{6}+\frac{1}{24}+\frac{1}{120}$$

Add 15 and 1 to get 16.

$$\frac{16}{6}+\frac{1}{24}+\frac{1}{120}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}+\frac{1}{24}+\frac{1}{120}$$

Least common multiple of 3 and 24 is 24. Convert \frac{8}{3} and \frac{1}{24} to fractions with denominator 24.

$$\frac{64}{24}+\frac{1}{24}+\frac{1}{120}$$

Since \frac{64}{24} and \frac{1}{24} have the same denominator, add them by adding their numerators.

$$\frac{64+1}{24}+\frac{1}{120}$$

Add 64 and 1 to get 65.

$$\frac{65}{24}+\frac{1}{120}$$

Least common multiple of 24 and 120 is 120. Convert \frac{65}{24} and \frac{1}{120} to fractions with denominator 120.

$$\frac{325}{120}+\frac{1}{120}$$

Since \frac{325}{120} and \frac{1}{120} have the same denominator, add them by adding their numerators.

$$\frac{325+1}{120}$$

Add 325 and 1 to get 326.

$$\frac{326}{120}$$

Reduce the fraction \frac{326}{120} to lowest terms by extracting and canceling out 2.

$$\frac{163}{60}$$

Factor

$$\frac{163}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{43}{60} = 2.716666666666667$$