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

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

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

li ke nha

A= 5/11.16 + 5/16.21 + .....+5/61.66

A = 1/5.(5/11 - 5/16 + 5/16 - .......5/66)

A = 1/5 . 25/66 = 5/66             

A = 5/11.16 + 5/16.21 + ... + 5/61/66

A = 1/11 - 1/16 + 1/16 - 1/21 + ... + 1/61 - 1/66

A = 1/11 - 1/66

A = 5/66

\(B=\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{61.66}\)

\(B=\dfrac{5}{5}\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)

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

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

\(B=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)

\(\frac{5}{66}\)    nha

\(B=\frac{5}{11.13}+\frac{5}{16.21}+...+\frac{5}{61.66}\)

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

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

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

\(\frac{5}{66}\)\(nha\)\(b\text{ạn}\)

\(theo\)\(mk\)\(l\text{à}\)\(th\text{ế}\)

\(ch\text{úc}\)\(b\text{ạn}\)\(h\text{ọc}\)\(t\text{ốt}\)

^_^ !

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

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

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

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

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

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

\(A=\frac{6}{66}-\frac{1}{66}\)

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

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

=\(\frac{5}{11}.\frac{5}{66}\)

=\(\frac{25}{726}\)

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

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

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

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

Vậy \(A=\frac{5}{66}\)

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

\(=5.\left(\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{61.66}\right)\)

\(=5.\frac{1}{4}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{24}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{5}{4}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{5}{4}.\frac{5}{66}\)

\(=\frac{25}{264}\)

Mình sửa lại đề nhé :))

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

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

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

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

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

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

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

D=\(\dfrac{4}{5}\)x\(\dfrac{5}{66}\)=\(\dfrac{2}{33}\)

Đặt:

\(A=\dfrac{7}{11\cdot16}+\dfrac{7}{16\cdot21}+\dfrac{7}{21\cdot26}+...+\dfrac{7}{61\cdot66}\)

\(\dfrac{5}{7}A=\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{61\cdot66}\)

\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{66}=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)

\(A=\dfrac{5}{66}\cdot\dfrac{7}{5}=\dfrac{7}{66}\)

\(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\)

=\(\frac{1}{5}.\frac{5}{11.16}+\frac{1}{5}.\frac{5}{16.21}+\frac{1}{5}.\frac{5}{21.26}+...+\frac{1}{5}.\frac{5}{61.66}\)

=\(\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)

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

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

=\(\frac{1}{5}.\left(\frac{6}{66}-\frac{1}{66}\right)=\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)

Đặt A = \(\frac{1}{11.16}+...+\frac{1}{61.66}\)

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

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

5a   =  \(\frac{1}{11}-\frac{1}{61}\)

5a   =  50/671

a     = \(\frac{50}{671}:5=\frac{10}{671}\)

\(\frac{1}{11.16}+\frac{1}{16.21}\)\(+\frac{1}{21.26}+...+\frac{1}{61.66}\)

= \(\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

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

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

= \(\frac{1}{5}.\left(\frac{5}{6}\right)\)

=\(\frac{1}{6}\)

k mk nha !

\(D=\frac{3}{11\cdot16}+\frac{3}{16\cdot21}+\frac{3}{21\cdot26}+....+\frac{3}{61\cdot66}\)

\(\frac{5}{3}D=\frac{5}{3}\left(\frac{3}{11\cdot16}+\frac{3}{16\cdot21}+\frac{3}{21\cdot26}+.....+\frac{3}{61\cdot66}\right)\)

\(\frac{5}{3}D=\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}+....+\frac{5}{61\cdot66}\)

\(\frac{5}{3}D=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\)

\(\frac{5}{3}D=\frac{1}{11}-\frac{1}{66}\)

\(\frac{5}{3}D=\frac{5}{66}\)

\(D=\frac{5}{66}:\frac{5}{3}=\frac{5}{66}\cdot\frac{6}{5}=\frac{1}{11}\)

D = 3/11.16 + 3/16.21 + 3/21.26 + ...... + 3/61.66

D = \(\frac{3}{5}\) . ( \(\frac{5}{11.16}\)+ \(\frac{5}{16.21}\)+......+\(\frac{5}{61.66}\) )

D = \(\frac{3}{5}\). ( \(\frac{1}{11}\)- \(\frac{1}{16}\) + \(\frac{1}{16}\)- \(\frac{1}{21}\)+ ......... + \(\frac{1}{61}\)- \(\frac{1}{66}\))

D =\(\frac{3}{5}\). ( \(\frac{1}{11}\)- \(\frac{1}{66}\))

D = \(\frac{3}{5}\). \(\frac{5}{66}\)

D = \(\frac{1}{22}\)

# HOK TỐT #

        \(D=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+...+\frac{3}{61.66}\)

<=> \(D=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)

<=> \(D=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)

<=> \(D=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{3}{5}.\frac{5}{66}=\frac{1}{22}\)

Vậy ...............