Question

 

Tìm x , biết :

1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ....... + 1/x.(x + 1) = 2018/2019

Giúp em nha !

Answer 1

1/1-1/2+1.2-1/3+1/3-1/4+..+1/x-1/x+1=2018/2019

1-1/x+1=2018/2019

1-2018/2019=1/x+1

1/2019=1/x+1

=>x+1=2019

=>x=2018

vậy...

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{2018}{2019}.\)

\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2018}{2019}.\)

\(\frac{1}{1}-\frac{1}{x+1}=\frac{2018}{2019}\)

\(\frac{1}{1}-\frac{2018}{2019}=\frac{1}{x+1}\)

\(\frac{1}{2019}=\frac{1}{x+1}\)

=> \(2019=x+1\)

\(x+1=2019\)

\(x=2019-1\)

\(x=2018\)

Vậy x = 2018