Solve 1/1*2+1/2*3+1/3*4+1/2019*2020

$$\frac{ 1 }{ 1 \cdot 2 } + \frac{ 1 }{ 2 \cdot 3 } + \frac{ 1 }{ 3 \times 4 } + \frac{ 1 }{ 2019 \cdot 2020 }$$

Evaluate

$$\frac{1529393}{2039190}\approx 0.750000245$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{1}{2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{2019\times 2020}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{2}+\frac{1}{6}+\frac{1}{3\times 4}+\frac{1}{2019\times 2020}$$

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

$$\frac{3}{6}+\frac{1}{6}+\frac{1}{3\times 4}+\frac{1}{2019\times 2020}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{6}+\frac{1}{3\times 4}+\frac{1}{2019\times 2020}$$

Add 3 and 1 to get 4.

$$\frac{4}{6}+\frac{1}{3\times 4}+\frac{1}{2019\times 2020}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{1}{3\times 4}+\frac{1}{2019\times 2020}$$

Multiply 3 and 4 to get 12.

$$\frac{2}{3}+\frac{1}{12}+\frac{1}{2019\times 2020}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{8}{12}+\frac{1}{12}+\frac{1}{2019\times 2020}$$

Since \frac{8}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{12}+\frac{1}{2019\times 2020}$$

Add 8 and 1 to get 9.

$$\frac{9}{12}+\frac{1}{2019\times 2020}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}+\frac{1}{2019\times 2020}$$

Multiply 2019 and 2020 to get 4078380.

$$\frac{3}{4}+\frac{1}{4078380}$$

Least common multiple of 4 and 4078380 is 4078380. Convert \frac{3}{4} and \frac{1}{4078380} to fractions with denominator 4078380.

$$\frac{3058785}{4078380}+\frac{1}{4078380}$$

Since \frac{3058785}{4078380} and \frac{1}{4078380} have the same denominator, add them by adding their numerators.

$$\frac{3058785+1}{4078380}$$

Add 3058785 and 1 to get 3058786.

$$\frac{3058786}{4078380}$$

Reduce the fraction \frac{3058786}{4078380} to lowest terms by extracting and canceling out 2.

$$\frac{1529393}{2039190}$$

Factor

$$\frac{1529393}{2 \cdot 3 \cdot 5 \cdot 101 \cdot 673} = 0.7500002451953962$$