tìm kiểu gì vậy

\(\Leftrightarrow x.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{1999}-\frac{1}{2000}\right)=1\)

\(\Leftrightarrow x.\left(1-\frac{1}{2000}\right)=1\Leftrightarrow x\cdot\frac{1999}{2000}=1\Leftrightarrow x=\frac{2000}{1999}\)

\(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2006.2007}=\frac{2006}{2007}\)

\(\frac{x}{1}-\frac{x}{2}+\frac{x}{2}-\frac{x}{3}+\frac{x}{3}-\frac{x}{4}+...+\frac{x}{2006}-\frac{x}{2007}=\frac{2006}{2007}\)

\(x-\frac{x}{2007}=\frac{2006}{2007}\)

\(\frac{2007x}{2007}-\frac{x}{2007}=\frac{2006}{2007}\)

\(2007x-x=2006\)

\(2006x=2006\)

\(x=1\)

theo mình x =1 không biết đúng không

theo suy luận của mình thì x sẽ bằng 1

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{19.20}-\frac{x}{40}=\frac{3}{-10}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-........-\frac{1}{20}-\frac{x}{40}=\frac{-3}{10}\)

\(\Rightarrow1-\frac{1}{20}-\frac{x}{40}=\frac{-3}{10}\)

\(\Rightarrow\frac{40}{40}-\frac{2}{40}-\frac{x}{40}=\frac{-12}{40}\)

\(\Rightarrow\frac{38}{40}-\frac{x}{40}=\frac{-12}{40}\)

\(\Rightarrow\frac{x}{40}=\frac{38}{40}-\frac{-12}{40}\)

\(\Rightarrow\frac{x}{40}=\frac{38}{40}+\frac{12}{40}\)

\(\Rightarrow\frac{x}{40}=\frac{50}{40}\)

\(\Rightarrow x=50\)

Vậy x = 50

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+..+\frac{1}{19\cdot20}-\frac{x}{40}=\frac{-3}{10}\)\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{19}-\frac{1}{20}-\frac{x}{40}=\frac{3}{-10}\)

\(1-\frac{1}{20}-\frac{x}{40}=\frac{3}{-10}\)

\(\frac{x}{40}=1-\frac{1}{20}-\frac{3}{-10}=1\frac{1}{4}=\frac{5}{4}\)

\(\frac{x}{40}=\frac{5}{4}\Rightarrow x=\frac{40\cdot5}{4}=50\)

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x(x+1)}=\frac{2019}{2020}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2019}{2020}\)

\(\Rightarrow1-\frac{1}{x+1}=\frac{2019}{2020}\)

\(\Rightarrow\frac{1}{x+1}=1-\frac{2019}{2020}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2020}\)

\(\Rightarrow x+1=2020\Leftrightarrow x=2019\)

Vậy x = 2019

Số x cần tìm là : 99

Ta có : \(\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+.....+\frac{5}{x\left(x+1\right)}=\frac{99}{20}\)

\(\Rightarrow5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{x\left(x+1\right)}\right)=\frac{99}{20}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{x}-\frac{1}{x+1}=\frac{99}{20}.\frac{1}{5}\)

\(\Rightarrow1-\frac{1}{x+1}=\frac{99}{100}\)

\(\Rightarrow\frac{1}{x+1}=1-\frac{99}{100}=\frac{1}{100}\)

=> x + 1 = 100

=> x = 99

Ta có  \(\frac{5}{1.2}+\frac{5}{2.3}+...+\frac{5}{x\left(x+1\right)}=\frac{99}{20}\)

   =>  \(5\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{99}{20}\)

   =>    \(5\left(1-\frac{1}{x+1}\right)=\frac{99}{20}\)

   =>   \(1-\frac{1}{x+1}=\frac{99}{100}\)

  =>   \(\frac{1}{x+1}=\frac{1}{100}\)

 =>   x+1 = 100

=>  x = 99

đề chưa đầy đủ

à đề thiếu tổng các giá trị tuyệt đối ở trên =100x

What wrong with you ?

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{\left(x-1\right)\times x}=\frac{15}{16}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x-1}-\frac{1}{x}=\frac{15}{16}\)

\(1-\frac{1}{x}=\frac{15}{16}\)

\(\frac{1}{x}=\frac{1}{16}\)

\(\Rightarrow x=16\)

= 1-1/x+1 = 17/18

=> 1/x+1 = 1-17/18= 1/18

=> x+1 = 18 => x=17

ta có 1/1.2+1/2.3+1/3.4+1/4.5+...+1/x.(x+1)=17/18

1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=17/18

1-1/x+1=17/18

1/x+1=1-17/18

1/x+1=1/18

suy ra: x+1=18

x=18-1

x=17