\(x-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}=\frac{1}{4.5}\)

\(x-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-\frac{1}{4.5}=0\)

\(x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\right)=0\)

\(x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)=0\)

\(x-\left(1-\frac{1}{5}\right)=0\)

\(x-\frac{4}{5}=0\)

\(x=\frac{4}{5}\)

\(x-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}=\frac{1}{4.5}\)

\(x-\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{3}\right)-\left(\frac{1}{3}-\frac{1}{4}\right)=\frac{1}{4}-\frac{1}{5}\)

\(x-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}=\frac{-1}{5}\)

\(x-1=-\frac{1}{5}\)

\(x=\frac{4}{5}\)

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

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

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

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

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

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

Vậy x = 2019

= 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

\(1+\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}+\frac{1}{2017\cdot2018}\)

\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}+\frac{1}{2017}-\frac{1}{2018}\)

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

\(=\frac{1009}{2018}-\frac{1}{2018}\)

\(=\frac{1008}{2018}=\)TỰ RÚT GỌN NHA

\(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2006.2007}+\frac{1}{2007.2008}\)

\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2007}-\frac{1}{2008}\)

\(=2-\frac{2007}{2008}\)

\(=\frac{2009}{2008}\)

~Học tốt~

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

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

=> 1/x+1 = 1/18

=> x + 1 = 18

=> x = 17 (tm)

Vậy x = 17 nha!

Ai mk mk lại !!

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

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

=>  1/x +1 = 1-17/18

=> 1/x+1 = 1/18

=> x= 17 

=>1-1/2+1/2-1/3+...+1/x-1/(x+1)=2022/2021

=>1-1/(x+1)=2022/2021

=>1/(x+1)=-1/2021=1/-2021

=>x+1=-2021

=>x=-2022