Question 128

The expression

$$\frac{1}{8} + \frac{1}{10} + \frac{1}{11} + \frac{1}{15} + \frac{1}{20} + \frac{1}{41} + \frac{1}{110} + \frac{1}{1640}$$ is equal to

Solution

Expression : $$\frac{1}{8} + \frac{1}{10} + \frac{1}{11} + \frac{1}{15} + \frac{1}{20} + \frac{1}{41} + \frac{1}{110} + \frac{1}{1640}$$

= $$(\frac{1}{41} + \frac{1}{1640}) + (\frac{1}{10} + \frac{1}{20}) + (\frac{1}{11} + \frac{1}{110}) + (\frac{1}{8} + \frac{1}{15})$$

= $$(\frac{40+1}{1640})+(\frac{2+1}{20})+(\frac{10+1}{110})+(\frac{15+8}{120})$$

= $$\frac{1}{40}+\frac{3}{20}+\frac{1}{10}+\frac{23}{120}$$

= $$\frac{3+18+12+23}{120}=\frac{56}{120}=\frac{7}{15}$$

=> Ans - (D)


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