Solve 1/1!+1/2!+1/3!

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

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

The factorial of 1 is 1.

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

Anything divided by one gives itself.

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

The factorial of 2 is 2.

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

Convert 1 to fraction \frac{2}{2}.

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

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

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

Add 2 and 1 to get 3.

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

The factorial of 3 is 6.

$$\frac{3}{2}+\frac{1}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{9}{6}+\frac{1}{6}$$

Since \frac{9}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{6}$$

Add 9 and 1 to get 10.

$$\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$