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

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

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

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

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 :))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 !

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

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

 \(A=\frac{1}{11}-\frac{1}{66}\)

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

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

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

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

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

\(B=\frac{6}{7}\)

_Học tốt nha_

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

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

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

A=\(\frac{1}{11}+0-\frac{1}{66}\)

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

A=11-16\11.16+21-16\21.16+...+66-61\61.66

A=1\11-1\16+1\16-...-1\66

A=1\11-1\66

A=5\66

nếu đúng thì like nhé

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

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

=(1/11-1/66)+0+..+0=1/11-1/66=6/66-1/66=5/66

vậy A=5/66

mk làm tắt dc ko

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

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

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

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

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

a/ \(A=\frac{1}{6}+\frac{1}{12}+.........+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{4}\)

b/ \(B=\frac{5}{11.16}+\frac{5}{16.21}+........+\frac{5}{61.66}\)

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

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

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

a) \(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(A=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

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

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

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

a) \(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(A=\frac{1}{2}-\frac{1}{8}\)

\(A=\frac{3}{8}\)

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

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

\(\Rightarrow B=\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{61.66}\)

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

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

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

\(A=5.\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{56.61}\right)\))

\(A=5.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{56}-\frac{1}{61}\right)\)

\(A=5.\left(\frac{1}{11}-\frac{1}{61}\right)\)

\(A=5.\frac{50}{671}\)

\(A=\frac{250}{671}\)

Chúc em học tốt^^

\(A=\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+.....+\frac{5^2}{56.61}\)

\(=5.\left(\frac{5}{11.16}+\frac{5}{16.21}+.....+\frac{5}{56.61}\right)\)

 \(=5.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{56}-\frac{1}{61}\right)\)

\(A=\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+...+\frac{5^2}{56.61}\)

\(A=5\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{56.61}\right)\)

\(A=5\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{56}-\frac{1}{61}\right)\)

\(A=5\left(\frac{1}{11}-\frac{1}{61}\right)\)

\(A=5.\frac{50}{671}\)

\(A=\frac{250}{671}\)