$a)\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{24.25}\\ =\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{24}-\dfrac{1}{25}\\ =\dfrac{1}{5}-\dfrac{1}{25}\\ =\dfrac{4}{25}\\ b)\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{99.101}\\ =\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\\ =1-\dfrac{1}{101}\\ =\dfrac{100}{101}\\ c)\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\\ =5\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\\ =5\left(\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\\ =5\left(\dfrac{1}{1}-\dfrac{1}{31}\right)\\ =\dfrac{150}{31}\\ d)\dfrac{4}{11.16}+\dfrac{4}{16.21}+...+\dfrac{4}{61.61}\\ =\dfrac{4}{5}\left(\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{61.61}\right)\\ =\dfrac{4}{5}\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\\ =\dfrac{4}{5}\left(\dfrac{1}{11}-\dfrac{1}{66}\right)\\ =\dfrac{2}{33}$
