\(B=\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+\frac{5}{24\cdot27}+...+\frac{5}{123\cdot126}\\ B=\frac{5}{3}\cdot\left(\frac{3}{18\cdot21}+\frac{3}{21\cdot24}+\frac{3}{24\cdot27}+...+\frac{3}{123\cdot126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{1}{18}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{7}{126}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\frac{1}{21}\\ B=\frac{5}{63}\)

Theo đề bài, ta có:

A = \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+...+\dfrac{6}{87.90}\)

A = \(2.\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+...+\dfrac{3}{87.90}\right)\)

A =\(2.\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)

A = \(2.\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)= \(\dfrac{1}{8}\)

A= \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+...+\dfrac{6}{87.90}\)

A= \(2\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+...+\dfrac{3}{87.90}\right)\)

A= \(2\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)

A= \(2\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)

A= 2. \(\dfrac{1}{16}\)

A= \(\dfrac{1}{8}\)

\(6.-\dfrac{5}{18}=-\dfrac{5}{3}\)

\(-\dfrac{13}{24}+-\dfrac{5}{21}.\dfrac{7}{25}=-\dfrac{13}{24}+-\dfrac{1}{15}=-\dfrac{73}{120}\)

\(-\dfrac{5}{13}-\dfrac{3}{26}.-\dfrac{2}{3}=-\dfrac{5}{13}-\left(-\dfrac{1}{13}\right)=-\dfrac{4}{13}\)

\(\left(\dfrac{2}{3}+-\dfrac{7}{6}\right).\left(\dfrac{3}{8}+-\dfrac{3}{24}\right)=-\dfrac{1}{2}.\dfrac{1}{4}=\dfrac{1}{8}\)

Kết quả lần lượt của các phép tính là :

\(\dfrac{-5}{3}\) , \(\dfrac{-73}{120}\) , \(\dfrac{-4}{13}\) , \(\dfrac{-1}{8}\)

a: 3/8=36/96

5/12=40/96

b: -2/9=-24/108

-5/12=-45/108

c: -3/16=-63/336

-5/24=-70/336

-21/56=-126/336

a) -3/7 + 5/13 + -4/7 = -3/7 + 4/7 + 5/13 = -1 + 5/13 = -13/13 + 5/13 = -8/13 b) -5/21 + -2/21 + 8/24 = -7/21 + 1/3 = -1/3 + 1/3 = 0

a) \(\dfrac{-3}{7}+\dfrac{5}{13}+\dfrac{-4}{7}\)

\(=\left(\dfrac{-3}{7}+\dfrac{-4}{7}\right)+\dfrac{5}{13}\)

\(=\left(-1\right)+\dfrac{5}{13}\)

\(=\dfrac{-8}{13}\)

b) \(\dfrac{-5}{21}+\dfrac{-2}{21}+\dfrac{8}{24}\)

\(=\left(\dfrac{-5}{21}+\dfrac{-2}{21}\right)+\dfrac{1}{3}\)

\(=\dfrac{-1}{3}+\dfrac{1}{3}\)

\(=0\)

\(A=-B\)

\(B=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{23.25}+\dfrac{2}{25.27}+\dfrac{1}{27}\)

\(B=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{23}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}\)

\(B=1\)

A=-1

\(A=-\dfrac{2}{1.3}-\dfrac{2}{3.5}-......-\dfrac{2}{25.27}-\dfrac{1}{27}\)

\(\Leftrightarrow A=-\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+.....+\dfrac{1}{27}\right)\)

\(\Leftrightarrow A=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}\right)\)

\(\Leftrightarrow A=-1\)

Ta có:5/20>5/25

5/21>5/25

5/22>5/25

5/23>5/25

5/24>5/25

=>S=5/20+5/21+5/22+5/23+5/24>5/25+5/25+5/25+5/25+5/25=1

=>5/20+5/21+5/22+5/23+5/24>1

DỄ

DO: 5/20 <1

5/21<1

5/22<1

5/23<1

5/24<1

=> 5/20+5/21+5/22+5/23+5/24<1

hay S<1 ( ĐPCM)

ĐÚNG NÈ ỦNG HỘ

d) 

` (-3)/7 + 5/13 + (-4)/7 =   -3/7 + (-4/7 )  + 5/13 = -1 + 5/13 = -8/13`

e2) 

`-5/21 + (-2)/21 + (-8)/4 = -7/21 + -8/4 = -7/3`

\(F=\dfrac{5}{6}+6\dfrac{5}{6}\left(11\dfrac{5}{20}-9\dfrac{1}{4}\right):8\dfrac{1}{3}\)

\(F=\dfrac{5}{6}+\dfrac{41}{6}\left(\dfrac{225}{20}-\dfrac{37}{4}\right):\dfrac{25}{3}\)

\(F=\dfrac{5}{6}+\dfrac{41}{6}.2.\dfrac{3}{25}\)

\(F=\dfrac{5}{6}+\dfrac{41}{25}.\dfrac{3}{25}\)

\(F=\dfrac{5}{6}+\dfrac{41}{25}\)

\(F=\dfrac{371}{150}\)

\(D=\left(\dfrac{136}{15}-\dfrac{28}{5}+\dfrac{62}{10}\right)\times\dfrac{21}{24}\)

\(D=\left(\dfrac{272}{30}-\dfrac{168}{30}+\dfrac{186}{30}\right)\times\dfrac{21}{24}\)

\(D=\dfrac{290}{30}\times\dfrac{21}{24}\)

\(D=\dfrac{29}{3}\times\dfrac{7}{8}\)

\(D=\dfrac{203}{24}\)