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\(\frac{4}{11.16}+\frac{4}{16.21}+...+\frac{4}{61.66}\)

\(=\frac{4}{11}-\frac{4}{16}+\frac{4}{16}-\frac{4}{21}+...+\frac{4}{61}-\frac{4}{66}\)

\(=\frac{4}{11}-\frac{4}{66}\)

\(=\frac{4}{11}-\frac{2}{33}\)

\(=\frac{12}{33}-\frac{2}{33}\)

\(=\frac{10}{33}\)

\(A=\frac{10}{11.16}+\frac{10}{16.21}+...+\frac{10}{61.66}\)

\(A=\frac{10}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

\(A=\frac{10}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(A=\frac{10}{5}\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{10}{5}.\frac{5}{66}=\frac{5}{33}\)

Vậy A =5/33

Bài 1:

 A  = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) +...+ \(\dfrac{1}{2019\times2021}\)

A =   \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\)+...+ \(\dfrac{2}{2019\times2021}\))

A = \(\dfrac{1}{2}\) \(\times\)( \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\)+...+ \(\dfrac{1}{2019}\) - \(\dfrac{1}{2021}\))

A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2021}\))

A = \(\dfrac{1010}{2021}\)

bạn có sử dụng discord không

Bài 2:

B = \(\dfrac{4}{11\times16}\) + \(\dfrac{4}{16\times21}\)+ \(\dfrac{4}{21\times26}\)+...+ \(\dfrac{4}{61\times66}\)
B = \(\dfrac{4}{5}\) \(\times\) ( \(\dfrac{5}{11\times16}\)+ \(\dfrac{5}{16\times21}\) + \(\dfrac{5}{21\times26}\)+...+ \(\dfrac{5}{61\times66}\))

B = \(\dfrac{4}{5}\) \(\times\) ( \(\dfrac{1}{11}\) - \(\dfrac{1}{16}\) + \(\dfrac{1}{16}\) - \(\dfrac{1}{21}\) + \(\dfrac{1}{21}\) - \(\dfrac{1}{26}\)+...+ \(\dfrac{1}{61}\) - \(\dfrac{1}{66}\))

B = \(\dfrac{4}{5}\) \(\times\)( \(\dfrac{1}{11}\) - \(\dfrac{1}{66}\))

B = \(\dfrac{4}{5}\) \(\times\)  \(\dfrac{5}{66}\)

B = \(\dfrac{2}{33}\)

E=\(\frac{1}{5}\).(\(\frac{1}{11}-\frac{1}{16}\)+\(\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\))

E=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)=\(\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)

\(E=\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)

\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(E=\frac{1}{5}.\frac{5}{66}\)

\(E=\frac{1}{66}\)

a) \(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\)

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

\(=1-\dfrac{1}{31}\)

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

b) \(\dfrac{4}{11\cdot16}+\dfrac{4}{16\cdot21}+...+\dfrac{4}{61\cdot66}\)

\(=\dfrac{4}{5}\cdot\left(\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{61\cdot66}\right)\)

\(=\dfrac{4}{5}\cdot\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)

\(=\dfrac{4}{5}\cdot\left(\dfrac{1}{11}-\dfrac{1}{66}\right)\)

\(=\dfrac{4}{5}\cdot\dfrac{5}{66}\)

\(=\dfrac{4}{66}\)

\(=\dfrac{2}{33}\)

a) A = 5²/(1.6) + 5²/(6.11) + ... + 5²/(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

b) B = 4/(11.16) + 4/(16.21) + ... + 4/(61.66)

= 4/5 .[5/(11.16) + 5/(16.21) + ... + 5/(61.66)]

= 4/5.(1/11 - 1/16 + 1/16 - 1/21 + ... + 1/61 - 1/66)

= 4/5.(1/11 - 1/66)

= 4/5 . 5/66

= 2/33

\(C=\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}=\frac{5}{5}\cdot\left(\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}\right)\)

\(=\frac{1}{5}\cdot\left(\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+...+\frac{5}{61\cdot66}\right)=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{1}{5}\cdot\left[\left(\frac{1}{11}-\frac{1}{66}\right)+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\)

\(=\frac{1}{5}\cdot\left[\left(\frac{6}{66}-\frac{1}{66}\right)+0+...+0\right]=\frac{1}{5}\cdot\frac{5}{66}=\frac{1\cdot5}{5\cdot66}=\frac{1\cdot1}{1\cdot66}=\frac{1}{66}\)

Vậy \(C=\frac{1}{66}\)

Chúc bạn học tốt!^_^

Ta có : \(C=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+......+\frac{2}{41.42}\)

\(C=2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{41.42}\right)\)

\(C=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{41}-\frac{1}{42}\right)\)

\(C=2\left(\frac{1}{3}-\frac{1}{42}\right)\)

\(C=2.\frac{13}{42}=\frac{13}{21}\)

Các bạn chỉ cần trả lời câu C thôi nha!!!

Ta có : \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+......+\frac{5}{61.66}\)

\(\Rightarrow A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{61}-\frac{1}{66}\)

\(\Rightarrow A=\frac{1}{11}-\frac{1}{66}\)

\(\Rightarrow A=\frac{5}{66}\)

a) \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

=> \(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

=> \(A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66

       = (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)

       = 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)

       = 25/66

b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

       = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

       = (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)

       = 1/1 - 1/7 = 6/7

c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21

   C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)

   C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]

   C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)

   C = 1

Dễ nhưng dài quá !

\(=11\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+\dfrac{5}{21\cdot26}+\dfrac{5}{26\cdot31}\right)\)

=11(1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31)

=11*25/186=275/186