`@ Alana`

$\dfrac{1}{1.4}$ `+` $\dfrac{1}{4.7}$ `+ ....+`$\dfrac{1}{x ( x+3 )}$ `= 675/2026`

`1/3 (` $\dfrac{3}{1.4}$ `+` $\dfrac{3}{4.7}$ `+ ....+`$\dfrac{3}{x ( x+3 )}$ `)` `= 675/2026`

`1/3 ( 1/1 - 1/4 + 1/4 - 1/7 +...+1/x - 1/(x+3) )` `= 675/2026`

`1/3 ( 1 - 1/(x+3) )` `= 675/2026`

`1 - 1/(x+3)` `= 675/2026 : 1/3`

`1 - 1/(x+3)` `= 2025/2026`

`1/(x+3)` `= 1 - 2025/2026`

`1/(x+3)` `= 1/2026`

`=> x+3 = 2026`

`x = 2023`