\(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+...+\dfrac{1}{9\times10}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\\=\dfrac{1}{2}-\dfrac{1}{10}\\ =\dfrac{10}{20}-\dfrac{2}{20}\\ =\dfrac{8}{20}\\ =\dfrac{2}{5}\)
