Question : The value of $(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90})$ is:
Option 1: $\frac{1}{10}$
Option 2: $\frac{3}{5}$
Option 3: $\frac{3}{20}$
Option 4: $\frac{7}{20}$
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Correct Answer: $\frac{3}{20}$
Solution :
$=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$
$=(\frac{1}{20}+\frac{1}{30})+(\frac{1}{42}+\frac{1}{56})+(\frac{1}{72}+\frac{1}{90})$
$=(\frac{3+2}{60})+( \frac{4+3}{168})+( \frac{5+4}{360})$
$=(\frac{1}{12})+( \frac{1}{24})+( \frac{1}{40})$
$=\frac{10+5+3}{120}$
$=\frac{18}{120}$
$=\frac{3}{20}$
Hence, the correct answer is $\frac{3}{20}$.
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