Question

3/1*6 + 3/6*11 + 3/11*16 +...+ 3/61*66

Answer 1

Đặt A = \(\dfrac{3}{1.6}+\dfrac{3}{6.11}+...+\dfrac{3}{61.66}\)

=> \(\dfrac{5}{3}A=\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{61.66}\)

=> \(\dfrac{5}{3}A=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

=> \(\dfrac{5}{3}A=1-\dfrac{1}{66}=\dfrac{65}{66}\)

=> A = \(\dfrac{13}{22}\)

@nam nguyen

Answer 2

Đặt :

\(Â=\dfrac{3}{1.6}+\dfrac{3}{6.11}+...............+\dfrac{3}{61.66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+..............+\dfrac{5}{61.66}\)

\(\Leftrightarrow A\dfrac{5}{3}=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+.........+\dfrac{1}{61}-\dfrac{1}{66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=1-\dfrac{1}{66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{65}{66}\)

\(\Leftrightarrow A=\dfrac{13}{22}\)

Answer 3

Đặt \(A=\dfrac{3}{1.6}+\dfrac{3}{6.11}+\dfrac{3}{11.16}+...+\dfrac{3}{61.66}\)

\(A=3.\dfrac{1}{5}.\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{61.66}\right)\)

\(A=\dfrac{3}{5}.\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)

\(A=\dfrac{3}{5}.\left(1-\dfrac{1}{66}\right)\)

\(A=\dfrac{3}{5}.\dfrac{65}{66}=\dfrac{13}{22}\)