\(\dfrac{55}{6x11}+\dfrac{55}{11x16}+\dfrac{55}{21x16}+\dfrac{55}{21x26}+\dfrac{55}{31x26}\)

\(=55\left(\dfrac{1}{6x11}+\dfrac{1}{11x16}+\dfrac{1}{21x16}+\dfrac{1}{21x26}+\dfrac{1}{31x26}\right)\)

\(=55\left(\dfrac{1}{5}x\left(\dfrac{1}{6}-\dfrac{1}{11}\right)+\dfrac{1}{5}x\left(\dfrac{1}{11}-\dfrac{1}{16}\right)+\dfrac{1}{5}x\left(\dfrac{1}{16}-\dfrac{1}{21}\right)+\dfrac{1}{5}x\left(\dfrac{1}{21}-\dfrac{1}{26}\right)+\dfrac{1}{5}x\left(\dfrac{1}{26}-\dfrac{1}{31}\right)\right)\)

\(=55x\dfrac{1}{5}x\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\right)\)

\(=11x\left(\dfrac{1}{6}-\dfrac{1}{31}\right)=11x\left(\dfrac{31-6}{186}\right)=11x\dfrac{25}{186}=\dfrac{275}{186}\)

C=\(\dfrac{55}{6\cdot11}\)+\(\dfrac{55}{11\cdot16}\)+\(\dfrac{55}{16\cdot21}\)+\(\dfrac{55}{21\cdot26}\)+\(\dfrac{55}{26\cdot31}\)

 =\(\dfrac{1}{6}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{16}\)+\(\dfrac{1}{16}\)-\(\dfrac{1}{21}\)+\(\dfrac{1}{21}\)-\(\dfrac{1}{26}\)+\(\dfrac{1}{26}\)-\(\dfrac{1}{31}\)

 =\(\dfrac{1}{6}\)-\(\dfrac{1}{31}\)=\(\dfrac{25}{186}\)

\(C=\dfrac{55}{6\times11}+\dfrac{55}{11\times16}+\dfrac{55}{16\times21}+\dfrac{55}{21\times26}+\dfrac{55}{26\times31}\)

\(\dfrac{1}{11}C=\dfrac{5}{6\times11}+\dfrac{5}{11\times16}+\dfrac{5}{16\times21}+\dfrac{5}{21\times26}+\dfrac{5}{26\times31}\)

\(\dfrac{1}{11}C=\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\)

\(\dfrac{1}{11}C=\dfrac{1}{6}-\dfrac{1}{31}=\dfrac{25}{186}\)

\(C=\dfrac{25}{186}:\dfrac{1}{11}=\dfrac{275}{186}\)

Ta có:

55/11x16+55/16x21+55/21x26x.....x55/36x41

=55/5 x (1/11-1/16+1/16-1/21+.......+1/36-1/41)

=55/5 x (1/11-1/41)

=55/5x30/451

=30/41

nhớ ****

\(\frac{A}{11}=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}+\frac{5}{31.36}+\frac{5}{36.41}\)

\(\frac{A}{11}=\frac{16-11}{11.16}+\frac{21-16}{16.21}+\frac{26-21}{21.26}+...+\frac{41-36}{36.41}\)

\(\frac{A}{11}=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{36}-\frac{1}{41}\)

\(\frac{A}{11}=\frac{1}{11}-\frac{1}{41}=\frac{30}{11.41}\Rightarrow A=\frac{11.30}{11.41}=\frac{30}{41}\)

\(\sqrt[1]{\dfrac{2}{3}_3\dfrac{1}{2}3_3\dfrac{3}{4}^3}\)

`A = 55/( 11xx16 ) + 55/( 16xx21 ) + 55/( 21xx26 ) + 55/( 26xx31) + 55/( 31xx36)+55/(36xx41)`

`A = 11 xx ( 5/( 11xx16 ) + 5/( 16xx21 ) + 5/( 21xx26 ) + 5/( 26xx31) + 5/( 31xx36)+5/(36xx41)`

`A = 11 xx ( 1/11 - 1/16 + 1/16 - 1/21 + 1/21 - 1/26 + 1/26 - 1/31 + 1/31 - 1/36 + 1/36 - 1/41 )`

`A = 11 xx ( 1/11 - 1/41 )`

`A = 1 - 11/41`

`A = 30/41` 

\(A=55.\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{36}+\dfrac{1}{36}-\dfrac{1}{41}\right)\)

\(A=55\times\left(\dfrac{1}{11}-\dfrac{1}{41}\right)=55\times\dfrac{30}{451}=\dfrac{150}{41}\)

30/41 bạn ạ

150/41 nha

\(\frac{55}{11\times6}+\frac{55}{16\times21}+\frac{55}{21\times26}+..+\frac{55}{36\times41}\)

\(=\frac{11-6}{11\times6}+\frac{21-16}{16\times21}+..+\frac{41-36}{36\times41}\)

\(=1-\frac{1}{11}+\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+..+\frac{1}{36}-\frac{1}{41}\)

\(=1-\frac{1}{41}\)

\(=\frac{40}{41}\)

40/41

\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+......+\frac{55}{36.41}\)

\(=11\left(\frac{5}{11.16}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)

\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{36}-\frac{1}{41}\right)\)

\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(=11.\frac{30}{451}=\frac{30}{41}\)

toán 5 | Diễn đàn HOCMAI - Cộng đồng học tập lớn nhất Việt Nam

\(A=\frac{55}{11X16}+\frac{55}{16X21}+\frac{55}{21X26}+\frac{55}{26X31}+\frac{55}{31X36}+\frac{55}{36X41}\)

\(A=11X\left(\frac{5}{11X16}+\frac{5}{16X21}+\frac{5}{21X26}+\frac{5}{26X31}+\frac{5}{31X36}+\frac{5}{36X41}\right)\)

\(A=11X\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}+\frac{1}{36}-\frac{1}{41}\right)\)

\(A=11X\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(A=11X\frac{1}{11}-11X\frac{1}{41}\)

\(A=1-\frac{11}{41}\)

\(A=\frac{30}{41}\)

\(A=\frac{55}{11x16}+\frac{55}{16x21}+\frac{55}{21x26}+\frac{55}{26x31}+\frac{55}{31x36}+\frac{55}{36x41}\)

\(A=11\left(\frac{5}{11x16}+\frac{5}{16x21}+\frac{5}{21x26}+\frac{5}{26x31}+\frac{5}{31x36}+\frac{5}{36x41}\right)\)

\(A=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}+\frac{1}{36}-\frac{1}{41}\right)\)

\(A=11\left(\frac{1}{11}-\frac{1}{41}\right)=1-\frac{11}{41}=\frac{30}{41}\)

Cảm ơn Trà My nhìu nha ^-^

\(\frac{55}{16.21}\)chứ nhỉ.

A=\(\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+\frac{55}{26.31}+\frac{55}{31.36}+\frac{55}{36.41}\)

A= 11.\(\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+....+\frac{1}{36}-\frac{1}{41}\right)\)

A= 11\(\left(\frac{1}{11}-\frac{1}{41}\right)\)

A= 11.\(\frac{30}{451}\)

A= \(\frac{30}{41}\)

\(\frac{30}{41}\)

\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+....+\frac{55}{36.41}\)

    \(=11.\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+.....+\frac{5}{36.41}\right)\)

     \(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{36}-\frac{1}{41}\right)\)

      \(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)

       \(=1-\frac{11}{41}\)

       \(=\frac{30}{41}\)