\(A=\frac{1}{7}.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{68}-\frac{1}{70}\right)\)

\(A=\frac{1}{7}.\left(\frac{1}{10}-\frac{1}{70}\right)=\frac{1}{7}.\frac{3}{35}=\frac{3}{245}\)

A=\(\frac{7}{10.11}\)+\(\frac{7}{11.12}\)+\(\frac{7}{12.13}\)+...+\(\frac{7}{69.70}\)

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

A=\(\frac{7}{10}-\frac{7}{70}\)

A=\(\frac{7}{10}-\frac{1}{10}\)

Ạ=\(\frac{6}{10}=\frac{3}{5}\).

\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+..+\frac{7}{69.70}\)

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

=\(7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{21}{35}\)

\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(\Rightarrow A=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{69.70}\right)\)

\(\Rightarrow A=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(\Rightarrow A=7\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(\Rightarrow A=7.\frac{3}{35}\)

\(\Rightarrow A=\frac{3}{5}\)

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

= \(\frac{3}{5}\)

H = \(\frac{7}{\text{10.11}}+\frac{7}{\text{11.12}}+\frac{7}{\text{12.13}}+...+\frac{7}{\text{69.70}}\)

H = 7 . \(\left(\frac{1}{\text{10.11}}+\frac{1}{\text{11.12}}+\frac{1}{\text{12.13}}+...+\frac{1}{\text{69.70}}\right)\)

H = 7 . \(\left(\frac{1}{\text{10}}-\frac{1}{11}+\frac{1}{\text{11}}-\frac{1}{12}+\frac{1}{\text{12}}-\frac{1}{13}+...+\frac{1}{\text{69}}-\frac{1}{70}\right)\)

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

H = 7 . \(\frac{3}{35}\)

H = \(\frac{3}{5}\)

\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

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

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

\(A=7.\frac{3}{35}\)

\(A=\frac{3}{5}\)

a = 7/10 x 11 + 7/11 x 12 + 7/12 x 13 + .....+ 7/69 x 70

a = 7/10 - 7/11 + 7/11 - 7/12 + 7/12 - 7/13 + 7/13 - ......+7/69 - 7/70

a= 7/10 - 7/70

a = 3/5

\(A=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)

suy ra \(A=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

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

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

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

\(A=\frac{3}{5}\)

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

A=1/10-1/70

A=3/35

OK

TÍCH MK NHÉ

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

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

A = 7.(1/10 - 1/70)

A = 7 . 6/10

A = 42/10 =21/5

*** k mk nhé các bn!

Đến chỗ 7.6/10 là A = 7.6/70 = 42/70  nha! Nhầm 1 chút,hì hì!

7/10 . 11 + 7/11.12 + 7/12.13 + ... + 7/69.70

= 7 ( 1/10.11 + 1/11.12 + 1/12.13 + ... + 1/69 . 70 )

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

= 7 ( 1/10 - 1/70 )

= 7 ( 7/70 - 1/70 )

= 7 . 6/70

= 42/70 

= 3/5 

Tk nha !!

=5.167

\(\frac{7}{10.11}+\frac{7}{11.12}+...+\frac{7}{69.70}\)

\(=\frac{7}{10}-\frac{7}{11}+\frac{7}{11}-\frac{7}{12}+...+\frac{7}{69}-\frac{7}{70}\)

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

\(=\frac{7}{10}-\frac{1}{10}\)\(=\frac{6}{10}=\frac{3}{5}\)