C=7/10x11+7/11x12+7/12x13+.................+7/69x70

C=1x7/10x11+1x7/11x12+...........+1x7/69x70

C=7(1/10x11+1/11x12+1/12x13+....+1/69x70)

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

C=7(1/10-1/70)

C=7(7/70-1/70)

C=7x6/70

C=3/5

`A=7/(10*11)+7/(11*12)+7/(12*13)+...+7/(69*70)`

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

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

`1/7A=1/10-1/70`

`1/7A=7/70-1/70`

`1/7A=6/70`

`A=3/5`

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

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

\(A=7\left(\dfrac{11-10}{10.11}+\dfrac{12-11}{11.12}+\dfrac{13-12}{12.13}+...+\dfrac{70-69}{69.70}\right)\)

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

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

\(A=7.\dfrac{3}{35}=\dfrac{3}{5}\)

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

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

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

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

      \(=7.\frac{3}{35}=\frac{3}{5}\)

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

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

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

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

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

C=7/10x11+7/11x12+7/12x13+.................+7/69x70

C=1x7/10x11+1x7/11x12+...........+1x7/69x70

C=7(1/10x11+1/11x12+1/12x13+....+1/69x70)

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

C=7(1/10-1/70)

C=7(7/70-1/70)

C=7x6/70

C=3/5

\(\frac{5}{11x12}+\frac{5}{12x13}+...+\frac{5}{98x99}\)

=\(\frac{5}{11}-\frac{5}{12}+\frac{5}{12}-\frac{5}{13}+...+\frac{5}{98}-\frac{5}{99}\)

=\(\frac{5}{11}-\frac{5}{99}\)

=\(\frac{40}{99}\)

Cái cuối bỏ 1 số 0 thì đúng hơn nha bạn

\(\frac{5}{11.12}+\frac{5}{12.13}+\frac{5}{13.14}+...+\frac{5}{98.99}\)

\(=5\left(\frac{1}{11.12}+\frac{1}{12.13}+\frac{1}{13.14}+...+\frac{1}{98.99}\right)\)

\(=5\left(\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{98}-\frac{1}{99}\right)\)

\(=5\left(\frac{1}{11}-\frac{1}{99}\right)\)

\(=5.\frac{8}{99}\)

\(=\frac{40}{99}\)

1/10×11 + 1/11×12 + 1/12×13 + ... + 1/999×1000

= 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + ... + 1/999 - 1/1000

= 1/10 - 1/1000

= 100/1000 - 1/1000

= 99/1000

1/10×11 + 1/11×12 + 1/12×13 + ... + 1/999×1000

= 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + ... + 1/999 - 1/1000

= 1/10 - 1/1000

= 100/1000 - 1/1000

= 99/1000

7/10x11+7/11x12+7/12x13+.................+7/69x70
=1x7/10x11+1x7/11x12+...........+1x7/69x70
=7(1/10x11+1/11x12+1/12x13+....+1/69x70)
=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)
=7x6/70

=3/5

NHỚ TK MK NHA

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

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

\(=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{7-1}{70}=\frac{6}{10}=\frac{3}{5}\)