Đặt: \(S=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+\dfrac{5^2}{11.16}+...+\dfrac{5^2}{26.31}\)
\(\Rightarrow\dfrac{S}{5}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{26.31}\\ =1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{26}-\dfrac{1}{31}\\ =1-\dfrac{1}{31}=\dfrac{30}{31}\\ \Rightarrow S=\dfrac{30}{31}.5=\dfrac{150}{31}\)
Sửa bài:
Đặt biểu thức là A. ta được:
\(\dfrac{A}{5}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\\ \dfrac{A}{5}=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\\ \dfrac{A}{5}=\dfrac{30}{31}\\ A=\dfrac{150}{31}.\)
\(\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\\ =5^2\left(\dfrac{1}{1.6}+\dfrac{1}{6.11}+...+\dfrac{1}{26.31}\right)\\ =5^2.\left(1-\dfrac{1}{6}+\dfrac{1}{6}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\\ =5^2.\left(1-\dfrac{1}{31}\right)\\ =5^2.\dfrac{30}{31}\\ =25.\dfrac{30}{31}\\ =\dfrac{750}{31}.\)
hiện tại em đang cần gấp lắm ạ 
