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

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

= \(\frac{3}{5}\)

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

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

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

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

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

vãi nồi :

S=7/10.11+7/11.12+...+7/69.70

=>S= 7.(1/10.11+1/11.12+...+1/69.70)

=> S=  7. ( 1/10-1/11+...+1/69-1/70)

=> S= 7. ( 1/10 - 1/70)

=> S = 7. 3/35

=> S = 3/5

We are one_Nguyễn Ngọc Sáng

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cậu kia làm sai rùi

A .1/5 = 1/10.11+1/11.12+1/12.13+...+1/99,100

A . 1/5 = 1/10-1/11+1/11-1/12+...+1/99-1/100

A .1/5 = 1/10-1/100

A.1/5 = 9/199

A = 9/20

k nhé

\(A=\frac{5}{10.11}+\frac{5}{11.12}+\frac{5}{12.13}+.....+\frac{5}{99.100}\)

=\(\frac{5}{10}-\frac{5}{11}+\frac{5}{11}-\frac{5}{12}+\frac{5}{12}-\frac{5}{13}\)

=\(\frac{5}{10}-\frac{5}{100}=\frac{45}{100}\)=\(\frac{9}{20}\)

\(A=\frac{5}{10.11}+\frac{5}{11.12}+\frac{5}{12.13}+.....+\frac{5}{99.100}\)

     \(=5.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{99.100}\right)\)

    \(=5.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{99}-\frac{1}{100}\right)\)

   \(=5.\left(1-\frac{1}{100}\right)\)

   \(=5.\frac{99}{100}=\frac{99}{20}\)

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

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

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

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

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

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

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

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

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

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