Question

1/3 + 1/6 + 1/10 + ..... + 2/x.(x+1)=1009/1010

Answer 1

X = 2019

Answer 2

Bạn giải cụ thể đi ạ

Answer 3

Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{1009}{1010}\)

=> \(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1009}{1010}\)

=> \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{1009}{1010}:2\)

=> \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{1009}{2020}\)

=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{1009}{2020}\)

=> \(\frac{1}{x+1}=\frac{1}{2020}\)

=> \(x+1=2020\)

=> x = 2019

Vậy x = 2019