Question

Tính giá trị của biểu thức: \(A=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\)

Answer 1

`A = ( 5^2 )/( 1*6)+(5^2)/(6*11)+.....+(5^2)/(26*31)`

   `= 5*(  5/( 1*6)+ 5/(6*11)+.....+5/(26*31))`

   `= 5*( 1 - 1/6 + 1/6 - 1/11 +....+1/26 - 1/31 )`

   `= 5*( 1 - 1/31 )`

   `= 5 * 30/31 = 150/31` 

Answer 2

\(A=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\)

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

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

\(=5.\left(1-\dfrac{1}{31}\right)=5.\dfrac{30}{31}=\dfrac{150}{31}\)