Question

x/1x2 +x/2x3 + x/3x4+ .....+x/2017x2018=-1

Answer 1

x= -2018/2017 

Answer 2

Bài làm:

Ta có: \(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2017.2018}=-1\)

\(\Leftrightarrow x\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\right)=-1\)

\(\Leftrightarrow x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\right)=-1\)

\(\Leftrightarrow x\left(1-\frac{1}{2018}\right)=-1\)

\(\Leftrightarrow x.\frac{2017}{2018}=-1\)

\(\Rightarrow x=-\frac{2018}{2017}\)

Answer 3

\(\frac{x}{1\cdot2}+\frac{x}{2\cdot3}+\frac{x}{3\cdot4}+...+\frac{x}{2017\cdot2018}=-1\)

=> \(\frac{x}{1}-\frac{x}{2}+\frac{x}{2}-\frac{x}{3}+...+\frac{x}{2017}-\frac{x}{2018}=-1\)

=> \(\frac{x}{1}-\frac{x}{2018}=-1\)

=> \(\frac{2018x-x}{2018}=-1\)

=> \(\frac{2017x}{2018}=-1\)

=> 2017x = -2018

=> x = -2018/2017

Answer 4

Ta có \(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2017.2018}=-1\)

=> \(x\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\right)=1\)

=> \(x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\right)=-1\)

=> \(x\left(1-\frac{1}{2018}\right)=-1\)

=> \(x.\frac{2017}{2018}=-1\)

=> \(x=-\frac{2018}{2017}\)

Vậy \(x=-\frac{2018}{2017}\)

Answer 5

\(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2017.2018}=-1\)

\(\Leftrightarrow x\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\right)=-1\)

\(\Leftrightarrow x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\right)=-1\)

\(\Leftrightarrow x\left(1-\frac{1}{2018}\right)=-1\Leftrightarrow\frac{2017x}{2018}=-1\Leftrightarrow x=-\frac{2018}{2017}\)

Answer 6

\(\frac{x}{1\cdot2}+\frac{x}{2\cdot3}+\frac{x}{3\cdot4}+...+\frac{x}{2017\cdot2018}=-1\)

\(\Rightarrow x\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2017.2018}\right)=1\)

\(\Rightarrow x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2017}-\frac{1}{2018}\right)=-1\)

\(\Rightarrow x\left(1-\frac{1}{2018}\right)=-1\)

\(\Rightarrow x.\frac{2017}{2018}=-1\)

\(\Rightarrow x=-\frac{2018}{2017}\)

Vậy ...........