Solve 1/2*3+1/3*4+1/4*5+1/98*99+frac{1}{99*100}=

$$\frac{ 1 }{ 2 \times 3 } + \frac{ 1 }{ 3 \times 4 } + \frac{ 1 }{ 4 \times 5 } + \frac{ 1 }{ 98 \times 99 } + \frac{ 1 }{ 99 \times 100 } =$$

Evaluate

$$\frac{1471}{4900}\approx 0.300204082$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{1}{6}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Multiply 3 and 4 to get 12.

$$\frac{1}{6}+\frac{1}{12}+\frac{1}{4\times 5}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Least common multiple of 6 and 12 is 12. Convert \frac{1}{6} and \frac{1}{12} to fractions with denominator 12.

$$\frac{2}{12}+\frac{1}{12}+\frac{1}{4\times 5}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Since \frac{2}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{12}+\frac{1}{4\times 5}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Add 2 and 1 to get 3.

$$\frac{3}{12}+\frac{1}{4\times 5}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

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

$$\frac{1}{4}+\frac{1}{4\times 5}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Multiply 4 and 5 to get 20.

$$\frac{1}{4}+\frac{1}{20}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Least common multiple of 4 and 20 is 20. Convert \frac{1}{4} and \frac{1}{20} to fractions with denominator 20.

$$\frac{5}{20}+\frac{1}{20}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Since \frac{5}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{20}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Add 5 and 1 to get 6.

$$\frac{6}{20}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}+\frac{1}{98\times 99}+\frac{1}{99\times 100}$$

Multiply 98 and 99 to get 9702.

$$\frac{3}{10}+\frac{1}{9702}+\frac{1}{99\times 100}$$

Least common multiple of 10 and 9702 is 48510. Convert \frac{3}{10} and \frac{1}{9702} to fractions with denominator 48510.

$$\frac{14553}{48510}+\frac{5}{48510}+\frac{1}{99\times 100}$$

Since \frac{14553}{48510} and \frac{5}{48510} have the same denominator, add them by adding their numerators.

$$\frac{14553+5}{48510}+\frac{1}{99\times 100}$$

Add 14553 and 5 to get 14558.

$$\frac{14558}{48510}+\frac{1}{99\times 100}$$

Reduce the fraction \frac{14558}{48510} to lowest terms by extracting and canceling out 2.

$$\frac{7279}{24255}+\frac{1}{99\times 100}$$

Multiply 99 and 100 to get 9900.

$$\frac{7279}{24255}+\frac{1}{9900}$$

Least common multiple of 24255 and 9900 is 485100. Convert \frac{7279}{24255} and \frac{1}{9900} to fractions with denominator 485100.

$$\frac{145580}{485100}+\frac{49}{485100}$$

Since \frac{145580}{485100} and \frac{49}{485100} have the same denominator, add them by adding their numerators.

$$\frac{145580+49}{485100}$$

Add 145580 and 49 to get 145629.

$$\frac{145629}{485100}$$

Reduce the fraction \frac{145629}{485100} to lowest terms by extracting and canceling out 99.

$$\frac{1471}{4900}$$

Factor

$$\frac{1471}{2 ^ {2} \cdot 5 ^ {2} \cdot 7 ^ {2}} = 0.30020408163265305$$