Solve 1+1/1+2+1/1+2+3+1/1+2+3+4

$$1+ \frac{ 1 }{ 1+2 } + \frac{ 1 }{ 1+2+3 } + \frac{ 1 }{ 1+2+3+4 }$$

Evaluate

$$\frac{8}{5}=1.6$$

Solution Steps

Add 1 and 2 to get 3.

$$1+\frac{1}{3}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}$$

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

$$\frac{3}{3}+\frac{1}{3}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}$$

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

$$\frac{3+1}{3}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}$$

Add 3 and 1 to get 4.

$$\frac{4}{3}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}$$

Add 1 and 2 to get 3.

$$\frac{4}{3}+\frac{1}{3+3}+\frac{1}{1+2+3+4}$$

Add 3 and 3 to get 6.

$$\frac{4}{3}+\frac{1}{6}+\frac{1}{1+2+3+4}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{8}{6}+\frac{1}{6}+\frac{1}{1+2+3+4}$$

Since \frac{8}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{6}+\frac{1}{1+2+3+4}$$

Add 8 and 1 to get 9.

$$\frac{9}{6}+\frac{1}{1+2+3+4}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}+\frac{1}{1+2+3+4}$$

Add 1 and 2 to get 3.

$$\frac{3}{2}+\frac{1}{3+3+4}$$

Add 3 and 3 to get 6.

$$\frac{3}{2}+\frac{1}{6+4}$$

Add 6 and 4 to get 10.

$$\frac{3}{2}+\frac{1}{10}$$

Least common multiple of 2 and 10 is 10. Convert \frac{3}{2} and \frac{1}{10} to fractions with denominator 10.

$$\frac{15}{10}+\frac{1}{10}$$

Since \frac{15}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{10}$$

Add 15 and 1 to get 16.

$$\frac{16}{10}$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$\frac{8}{5}$$

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$