a, 

suy ra A = 7. (1/10.11+1/11.12+1/12.13+.......+1/69.70)

suy ra A = 7. ( 1/10 - 1/11+ 1/11 - 1/12 + 1/12 - 1/13+ ............. + 1/69 - 1/70)

suy ra A = 7. ( 1/ 10 - 1/70) 

suy ra  A= 7. 3/35

suy ra A= 3/5

mấy câu kia tương tự bạn nhá

A=\(\frac{1}{7}\)x(\(\frac{1}{10}\)+\(\frac{1}{11}\)+\(\frac{1}{11}\)+\(\frac{1}{12}\)+\(\frac{1}{12}\)+\(\frac{1}{13}\)+......+\(\frac{1}{69}\)+\(\frac{1}{70}\))

A=\(\frac{1}{7}\)x(\(\frac{1}{10}\)+\(\frac{1}{70}\))

A=\(\frac{1}{7}\)x(\(\frac{7}{70}\)+\(\frac{1}{70}\))

A=\(\frac{1}{7}\)x\(\frac{4}{35}\)

A=\(\frac{4}{245}\)

1) A=7/10.11+7/11.12+7/12.13+...+7/69.70

  A=7.(1/10.11+1/11.12+1/12.13+...+1/69.70)

 A= 7.(1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70)

 A= 7.(1/10-1/70)

 A=7.3/35=3/5

2)B=1/25.27+1/27.29+1/29.31+...+1/73.1/75

  B=1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75

  B=1/25-1/75=2/75

A = 7/ 10.11 + 7/ 11.12 + 7/ 12.13 + .... + 7/69.70

(1/7).A=1/10.11+1/11.12+...+1/69.70

=1/10-1/11+1/11-1/12+...+1/69-1/70

=1/10-1/70=3/35

=>A=7.(3/35)

=3/5

2 ) B = 1/ 25.27 + 1/ 27.29 + 1/29.31+ ......+ 1/ 73.75

=>(1/2).B=2/25.27+...+2.73.75

=1/25-1/27+...+1/73-1/75

=1/25-1/75

=2/75

=>B=4/75

 A=7.(1/10.11+1/11.12+1/12.13+...+1/69.70)

 A= 7.(1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70)

 A= 7.(1/10-1/70)

 A=7.3/35=3/5

2)B=1/25.27+1/27.29+1/29.31+...+1/73.1/75

  B=1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75

  B=1/25-1/75=2/75

A=.....

=\(7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{69.70}\right)=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+.....+\frac{1}{69}-\frac{1}{70}\right)\)

=\(7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)

MẤY PHẦN SAU CX TÁCH MẪU RA RÙI LÀM NHƯ VẬY

TỰ LÀM NHE

\(B=\frac{1}{3\cdot6}+\frac{1}{6\cdot9}+...+\frac{1}{30\cdot33}\)

\(B=\frac{1}{3}\cdot\left(\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+...+\frac{3}{30\cdot33}\right)\)

\(B=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\right)\)

\(B=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{33}\right)\)

\(B=\frac{1}{3}\cdot\frac{10}{33}=\frac{10}{99}\)

\(C=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\)

\(C=\left(1-\frac{1}{1\cdot2}\right)+\left(1-\frac{1}{2\cdot3}\right)+...+\left(1-\frac{1}{9\cdot10}\right)\)

\(C=9-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\right)\)

\(C=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(C=9-\left(1-\frac{1}{10}\right)\)

\(C=9-\frac{9}{10}=\frac{81}{10}\)

các bạn đều sai hết mà các bạn lại cho những câu hỏi đó đúng 

= 7.( \(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-....-\frac{1}{70}\))

= 7.( \(\frac{1}{10}-\frac{1}{70}\))

= 7.(\(\frac{7}{70}-\frac{1}{70}\))

= 7.\(\frac{6}{70}\)

= \(\frac{3}{5}\)

 C=4/2.4+4/4.6+4/6.8+...+4/2008.2010
 C = 2 ( 2 / 2.4 + 2/4.6 + 2/6.8 + ...+2/2008.2010)
 C = 2 ( 1 - 1/4 + 1/4 - 1/6+1/6 - 1/8 +....+1/2008 - 1/2010 )
 C = 2 ( 1 - 1 / 2010 )
 C = 2 . 2009/2010 
 C = 2009 / 1005
Chúc bạn học tốt !

bạn tách ra từng bài một mình sẽ giúp 

B = \(\frac{1}{25.27}\)+ \(\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
2B = 2 ( 1/25.27+1/27.29+1/29.31+...+1/73.75)  Mình x 2 lên tí phải chia cho 2
2B = \(\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
2B = 1/25 - 1/27+ 1/27-1/29 + .... + 1/73 - 1/75
2B = 1/25 - 1/75
2B = 3/75 - 1/75
2B = 2/75
=> B = 2/75 : 2
  B = 2/75 . 1/2
  B = 1/75
Chúc bạn học tốt 

a, \(A=\frac{6}{10.11}+\frac{6}{11.12}+\frac{6}{12.13}+...+\frac{6}{69.70}\)

\(A=\frac{6}{10}-\frac{6}{11}+\frac{6}{11}-\frac{6}{12}+\frac{6}{12}-\frac{6}{13}+...+\frac{6}{69}-\frac{6}{70}\)

\(A=\frac{6}{10}-\frac{6}{70}\)

\(A=\frac{18}{35}\)

b, \(B=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2018.2020}\)

\(B=\frac{4}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2018.2020}\right)\)

\(B=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)

\(B=2.\left(\frac{1}{2}-\frac{1}{2020}\right)\)

\(B=2.\frac{1009}{2020}\)

\(B=\frac{1009}{1010}\)

Chúc bạn học tốt