`(6/7+1/4):(19/4-1/4) <x<7/3`

`(24/28+7/28):18/4<x<7/3`

`31/28:18/4<x<7/3`

`31/28 ×4/18 < x < 7/3`

` 31/126 < x < 7/3`

`0, 246 < x  < 2,333`

Vì `x∈N⇒ x=1` hoặc `x=2.`

Vậy `x∈N⇒ x=1` hoặc `x=2.`

`1/3+1/6+1/10+…………+\frac{2}{x×(x+1)}=1009/1010 `

`2/6 + 2/12 + 2/20+ …………+\frac{2}{x×(x+1)}=1009/1010 `

` 2× (1/6 + 1/12 + 1/20 +…+ \frac{1}{x×(x+1)})=1009/1010 `

` 2× (\frac{1}{2×3}+ \frac{1}{3×4}+ \frac{1}{4×5} +…+ \frac{1}{x×(x+1)})=1009/1010 `

` 2× (1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/x –  \frac{1}{x+1))=1009/1010 `

`  1/2 –  \frac{1}{x+1}=1009/1010 : 2  `

`  1/2 –  \frac{1}{x+1}=1009/1010 × 1/2  `

`  1/2 –  \frac{1}{x+1}=1009/2020  `

`  \frac{1}{x+1} = 1/2 – 1009/2020 `

`  \frac{1}{x+1} = 1010/2020 – 1009/2020 `

`  \frac{1}{x+1} = 1/2020  `

`⇒ x+1 = 2020 `

` x = 2020 – 1`

`x = 2019` ( Thỏa mãn `x` là số tự nhiên )

Vậy `x=2019.`