Mình nói lí thuyết cho nghe:

 Với phân số \(\frac{a-b}{a.b}\)\(\left(VD:\frac{1}{1.2};\frac{1}{2.3};\frac{1}{2015.2016};\frac{3}{15.18};\frac{3}{18.21};\frac{1}{10.11};\frac{1}{11.12};...\right)\)thì:

 \(\frac{b-a}{a.b}=\frac{b}{a.b}-\frac{a}{a.b}=\frac{1}{a}-\frac{1}{b}\left(VD:\frac{1}{1.2}=\frac{1}{1}-\frac{1}{2};\frac{3}{15.18}=\frac{1}{15}-\frac{1}{18}\right)\)

ÁP dụng để tính:

 c) \(\Rightarrow\frac{1}{4}C=\frac{1}{4}\left(\frac{12}{15.18}+\frac{12}{18.21}+...+\frac{12}{87.90}\right)=\frac{3}{15.18}+\frac{3}{18.21}+....+\frac{3}{87.90}\)

\(\Rightarrow\frac{1}{4}C=\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}=\frac{1}{15}-\frac{1}{90}\)

=> \(C=\left(\frac{1}{15}-\frac{1}{90}\right).4\)

a,\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2015}-\frac{1}{2016}\)

\(A=1-\frac{1}{2016}\)suy ra \(A=\frac{2015}{2016}\)

b, \(B=5\left(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{69.70}\right)\)

\(B=5\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

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

\(B=\frac{3}{7}\)

c,\(C=4.\left(\frac{3}{15.18}+\frac{3}{18.21}+...+\frac{3}{87.90}\right)\)

\(C=4.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(C=4.\left(\frac{1}{15}-\frac{1}{90}\right)\)suy ra \(C=4.\frac{1}{18}\)

\(C=\frac{2}{9}\)

a) \(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2015.2016}\)

\(A=1.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)

\(A=1.\left(1-\frac{1}{2016}\right)\)

\(A=1.\frac{2015}{2016}\)

\(A=\frac{2015}{2016}\)

b) \(B=\frac{5}{10.11}+\frac{5}{11.12}+...+\frac{5}{69.70}\)

\(B=5.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(B=5.\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(B=5.\frac{3}{35}\)

\(B=\frac{3}{7}\)

c) \(C=\frac{12}{15.18}+\frac{12}{18.21}+...+\frac{12}{87.90}\)

\(C=4.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(C=4.\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(C=4.\frac{1}{18}\)

\(C=\frac{2}{9}\)

\(\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+.......+\frac{1}{19\cdot20}\)\(=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+.....+\frac{1}{18}-\frac{1}{19}\)\(+\frac{1}{19}-\frac{1}{20}\)

                                                                       \(=\frac{1}{10}-\frac{1}{20}=\frac{2}{20}-\frac{1}{20}=\frac{1}{20}\)

K CHO MÌNH NHA CÁC BẠN

= 1/10-1/11+...+1/19-1/20

=1/10-1/20=1/10

A = \(\frac{1}{10\times11}+\frac{1}{11\times12}+...+\frac{1}{19\times20}\)

A = \(\frac{11-10}{10\times11}+\frac{12-11}{11\times12}+...+\frac{20-19}{19\times20}\)

A = \(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{19}-\frac{1}{20}\)

A = \(\frac{1}{10}-\frac{1}{20}\)

A = \(\frac{1}{20}\)

A = 0,05

Nếu mình đúng thì các bạn k mình nhé

caau hoi tuong tu cungx cos

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 

Lưu ý : . là dấu nhân

ai làm đúng , nhanh mình k

bình chọn đúng

\(S=\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{99.100}\)

\(=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{10}-\frac{1}{100}=\frac{9}{100}\)

Dấu chấm là dấu nhân !!!

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

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

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

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

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

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

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

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

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

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

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

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

= \(\frac{3}{5}\)

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

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

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

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

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