Question

Answer 1

\(=\dfrac{3}{5}\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{101\cdot106}\right)\)

\(=\dfrac{3}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)

\(=\dfrac{3}{5}\cdot\dfrac{105}{106}=\dfrac{63}{106}\)

Answer 2

\(=\dfrac{3}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)=\dfrac{3}{5}.\dfrac{105}{106}=\dfrac{63}{106}\)