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

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

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

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

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

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

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

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

\(B=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)\)

\(=\frac{1}{2}.\frac{2}{75}\)

\(=\frac{1}{75}\)

=

vậy 4A=4/2-4/4-4/6+...+4/46-4/48-4/50

4A=48/25

A=12/25

\(\left(\frac{4}{2.4}+\frac{4}{4.6}+.....+\frac{4}{4020.4022}\right)x=2010\)

\(\Leftrightarrow2x\left(\frac{2}{2.4}+\frac{2}{4.6}+....+\frac{2}{4020.4022}\right)=2010\)

\(\Leftrightarrow2x\left(\frac{1}{2}-\frac{1}{4}+.....+\frac{1}{4020}-\frac{1}{4022}\right)=2010\)

\(\Leftrightarrow2x\left(\frac{1}{2}-\frac{1}{4022}\right)=2010\)

Tự biên tự diễn

Ko chép lại đề nhé

<=> 2( 2/2.4 + 2/2.6 + 2/2.8 +...+ 2/ 4020.4022) x= 2010

<=> 2( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 +....+ 1/4020- 1/4022 )x=2010

<=> ( 1/2 - 1/4022)2x = 2010

<=> ( 2011/4022 - 1/4022 )2x = 2010

<=>( 2010/4022) .2x= 2010

<=> 2x = 2010 : 2010/4022

<=> 2x = 4022

=> x = 2011 

Vậy x = 2011

ĐKXĐ:  \(x\ne0;x\ne-2\)

\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)

\(\Leftrightarrow\)\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)

\(\Leftrightarrow\)\(\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\)

\(\Leftrightarrow\)\(\frac{1}{x+2}=\frac{1}{18}\)

\(\Rightarrow\)\(x+2=18\)

\(\Leftrightarrow\)\(x=16\) (t/m ĐKXĐ)

Vậy...

1/2(1-1/4+1/4-1/6+1/6-1/8+...+1/x-1/x+2)=4/9

1/2(1-1/x+2)=4/9

1-  1/x+2=4/9:1/2

1  -  1  /x+2=8/9

1/x+2=1-8/9

1/x+2=1/9

suy ra x+2=9

        x=9-2

        x=7

\(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+................+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\Rightarrow\frac{x+2-2}{2x+4}=\frac{4}{9}\Rightarrow9x=8x+16\)

\(\Rightarrow x=16\)

\(E=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+....+\frac{1}{2016.2018}\)

\(E=\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2018-2016}{2016.2018}\)

\(2E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(E=\left(\frac{1}{2}-\frac{1}{2018}\right).\frac{1}{2}\)

\(E=\frac{504}{1009}.\frac{1}{2}\)

\(E=\frac{252}{1009}\)

\(E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(E=\frac{1}{2}-\frac{1}{2018}\)

\(E=\frac{1005}{2018}\)

\(E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2116}-\frac{1}{2018}\)

\(E=\frac{1}{2}-\frac{1}{2018}\)

\(E=\frac{1005}{2018}\)

Ô phép tính khủng. Cái này do bạn chế ra à !
 

khủng chưa My Shipfriend

\(\frac{3}{2.4}+\frac{3}{4.6}+....+\frac{3}{98.100}\)

\(=\frac{3}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)

\(=\frac{3}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\right)\)

\(=\frac{3}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{3}{2}.\frac{49}{100}=\frac{147}{200}\)

\(\frac{3}{2.4}+\frac{3}{4.6}+\frac{3}{6.8}+...+\frac{3}{98.100}\)

\(=\frac{3}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{98.100}\right)\)

\(=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{98}-\frac{1}{100}\right)\)

\(=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{3}{2}.\frac{49}{100}=\frac{147}{200}\)

Đặt \(A=\frac{3}{2.4}+\frac{3}{4.6}+\frac{3}{6.8}+...+\frac{3}{98.100}\)

\(A=\frac{3}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\right)\)

\(A=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(A=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(A=\frac{3}{2}.\frac{49}{100}\)

\(A=\frac{147}{200}\)

Vậy \(A=\frac{147}{200}\)

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