\(S=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+...+\dfrac{1}{304\cdot307}\)
\(3S=\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{304\cdot307}\)
\(\)\(3S=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{304}-\dfrac{1}{307}\)
\(3S=1-\dfrac{1}{307}\)
\(3S=\dfrac{306}{307}\)
\(S=\dfrac{306}{307}\cdot\dfrac{1}{3}\)
\(S=\dfrac{102}{307}\)
\(S=\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{304.307}\)
\(S=\dfrac{1}{3}\left(1-\dfrac{1}{4}\right)+\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}\right)+...+\dfrac{1}{3}\left(\dfrac{1}{304}-\dfrac{1}{307}\right)\)
\(S=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...-\dfrac{1}{304}+\dfrac{1}{304}-\dfrac{1}{307}\right)\)
\(S=\dfrac{1}{3}\left(1-\dfrac{1}{307}\right)\)
\(S=\dfrac{1}{3}.\dfrac{306}{307}\)
\(S=\dfrac{102}{307}\)
