\(\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}-...-\dfrac{1}{9\cdot10}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}-\left(\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=\dfrac{1}{3}-\dfrac{1}{2}+\dfrac{1}{10}\)
\(=\dfrac{10}{30}-\dfrac{15}{30}+\dfrac{3}{30}\)
\(=\dfrac{-1}{15}\)