\(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\cdot\cdot\cdot+\dfrac{1}{120}\)
\(A=\dfrac{2}{2}\left(\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\cdot\cdot\cdot+\dfrac{1}{120}\right)\)
\(A=\dfrac{2}{1}\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\cdot\cdot\cdot+\dfrac{1}{240}\right)\)
\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\cdot\cdot\cdot+\dfrac{1}{15.16}\right)\)
\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\cdot\cdot\cdot+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(A=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)
\(A=2\left(\dfrac{4}{16}-\dfrac{1}{16}\right)\)
\(A=2.\dfrac{3}{16}\)
\(A=\dfrac{3}{8}\)
