Question

$\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}$ is equal to : __.

• A. $\frac{2}{27}$
• B. $\frac{1}{9}$
• C. $\frac{6}{55}$
• D. $\frac{5}{27}$

Answer 1

The correct option is C $\frac{6}{55}$

Given expression
$\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}$
can be written as
$\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}....+\frac{1}{10}-\frac{1}{11}$

$=\frac{11-5}{55}=\frac{6}{55}$