\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

\(\frac{5^2}{1.6}=5.\left(\frac{1}{1}-\frac{1}{6}\right)\)

\(\frac{5^2}{6.11}=5.\left(\frac{1}{6}-\frac{1}{11}\right)\)

............................

\(\frac{5^2}{26.31}=5.\left(\frac{1}{26}-\frac{1}{31}\right)\)

cộng hết lại: \(5.\left(\frac{1}{1}-\frac{1}{31}\right)=5\left(\frac{30}{31}\right)=\frac{150}{31}\)

Ta có : 

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)

\(=\)\(5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)

\(=\)\(5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(=\)\(5\left(1-\frac{1}{31}\right)\)

\(=\)\(5-\frac{5}{31}\)

\(=\)\(\frac{150}{31}\)

Chúc bạn học tốt ~ 

\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{1}{26.31}\)

    \(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

    \(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)

 \(=1-\frac{1}{31}=\frac{31-1}{31}\)

\(=\frac{30}{31}\)

Vậy \(A=\frac{30}{31}\)

\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{31}\)

\(\Rightarrow A=\frac{30}{31}\)

\(\Rightarrow A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+.....+\frac{1}{26}-\frac{1}{31}\)

\(\Rightarrow A=1-\frac{1}{31}\)

\(\Rightarrow A=\frac{30}{31}\)

\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)

\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

\(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)

\(=1-\frac{1}{31}=\frac{31-1}{31}=\frac{30}{31}\)

\(\text{Vậy }A=\frac{30}{31}\).

A = \(\frac{5}{1x6}+\frac{5}{6x11}+\frac{5}{11x16}+...+\frac{5}{26x31}\)

A=  \(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

A = \(\frac{1}{1}-\frac{1}{31}=\frac{31}{31}-\frac{1}{31}=\frac{30}{31}\)

mk chỉnh lại đề nhé, có lẽ bn ghi thiếu:

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}+\frac{5^2}{31.36}\)

\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}+\frac{5}{31.36}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}\right)\)

\(=5\left(1-\frac{1}{36}\right)=5.\frac{35}{36}=\frac{175}{36}\)

Đề đúng:

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}+\frac{5^2}{31.36}\)

\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}+\frac{5}{31.36}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}\right)\)

\(=5\left(1-\frac{1}{36}\right)\)

\(=5\left(\frac{36}{36}-\frac{1}{36}\right)\)

\(=5.\frac{35}{36}\)

\(=\frac{175}{36}\)

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)

\(=5^2\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}\right)\)

\(=25.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right)\)

\(=5\left(1-\frac{1}{26}\right)\)

\(=5.\frac{25}{26}\)

\(=\frac{125}{26}\)

ko tin là học lớp 1 đâu ^{(lớp 1 ko đc học cái này)}