c/
C = 1/100-1/100-1/99-1/99-1/98-1/98-1/97-..........-1/3-1/2-1/2-1/1
C = 1/100-1/100-1/1
C = 0-1/1
C = -1

có 2 cách làm mà mik làm 1 cách thôi nha !

        A = (6 - 2/3 + 1/2) - (5 + 5/3 - 3/2) - (3 -7/3 + 5/2)

           = ( 36/6 - 4/6 + 3/6 ) - ( 150/30 + 50/30 +45/30 ) - ( 18/6 - 14/6 + 15/6 )

           =          35/6                    -        155/30           -       19/6          = 35/6 - 19/6 - 155/30

          = 16/6 - 155/30 = 80/30 - 155/30 = 75/30 = - 5/2 

Hơi khó nhìn. Chúc hok tốt !

hong ai giúp mik dọ? ;-;

\(A=\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{13\times15}\)

\(2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}\)

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

\(2A=\dfrac{14}{15}\)

\(A=\dfrac{7}{15}\)

\(A=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{13\cdot15}\)

\(\Rightarrow2A=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{13\cdot15}\)

\(\Rightarrow2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}\)

\(\Rightarrow2A=1-\dfrac{1}{15}\)

\(\Rightarrow A=-\dfrac{1}{14}:2\)

\(\Rightarrow A=-\dfrac{1}{28}\)

Mình sửa lại tí nhé:

\(\Rightarrow2A=\dfrac{14}{15}\)

\(\Rightarrow A=\dfrac{14}{15}:2\)

\(\Rightarrow A=\dfrac{7}{15}\)

a) \(5+\dfrac{2}{3}=\dfrac{15}{3}+\dfrac{2}{3}=\dfrac{17}{3}\)

b) \(\dfrac{12}{5}\cdot\dfrac{1}{4}=\dfrac{3}{5}\)

c) \(\dfrac{3}{8}-\dfrac{1}{3}=\dfrac{9}{24}-\dfrac{8}{24}=\dfrac{1}{24}\)

d) \(\dfrac{6}{15}-\dfrac{1}{3}:\dfrac{5}{3}=\dfrac{6}{15}-\dfrac{1}{3}\cdot\dfrac{3}{5}=\dfrac{6}{15}-\dfrac{1}{5}=\dfrac{6}{15}-\dfrac{3}{15}=\dfrac{3}{15}=\dfrac{1}{5}\)

\(5+\dfrac{2}{3}=\dfrac{5}{1}+\dfrac{2}{3}=\dfrac{15}{3}+\dfrac{2}{3}=\dfrac{17}{9};\dfrac{12}{5}x\dfrac{1}{4}=\dfrac{12}{40};\dfrac{3}{8}-\dfrac{1}{3}=\dfrac{9}{24}-\dfrac{8}{24}=\dfrac{1}{24}\)

\(\dfrac{6}{15}-\dfrac{1}{3}:\dfrac{5}{3}=\dfrac{6}{15}-\dfrac{3}{15}=\dfrac{3}{15}=\dfrac{1}{3}\)

 = 6 - (5+3) - (2/3 + 5/3 -7/3) + ( 1/2 + 3/2 -5/2 ) 
= 6 - 8 - 0 - 1/2 
= -2 - 1/2 
= -2/1/2

A = 6 - 2/3 + 1/2 - 5 - 5/3 + 3/2 - 3 + 7/3 - 5/2 

A = ( 6 - 5 - 3 ) + ( -2/3 - 5/3 + 7/3 ) + ( 1/2 + 3/2 - 5/2 )

A = ( -2 ) +  0  + ( -1/2 )

A = ( -2 ) + ( -1/2 )

A = -5/2

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

    \(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

     \(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.95}\)

   \(=\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{92-92}{92.95}\)

   \(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{92}-\frac{1}{95}\)

     \(=\frac{1}{2}-\frac{1}{95}=\frac{93}{190}\)

\(C=\frac{5}{6}+\frac{5}{66}+\frac{5}{176}+\frac{5}{336}\)

    \(=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}\)

    \(=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}\) 

    \(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}\)

     \(=1-\frac{1}{21}=\frac{20}{21}\)

[ HỌC TỐT]

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=\frac{1}{2}-\frac{1}{100}\)

\(A=\frac{100}{200}-\frac{2}{200}\)

\(A=\frac{98}{200}=\frac{49}{100}\)

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.95}\)

\(B=\frac{3}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{92}-\frac{1}{95}\right)\)

\(B=\frac{1}{2}-\frac{1}{95}=\frac{93}{190}\)