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