Question Number 157660 by naka3546 last updated on 26/Oct/21
![Given x_1 = 1, x_2 , x_3 , …, is a real numbers sequence for n ≥ 1 with recurrence relation x_(n+1) − x_n = (1/(2x_n )) . [x] is expressed as the largest integer of x . [25x_(625) ] = ?](https://www.tinkutara.com/question/Q157660.png)
$${Given}\:\:{x}_{\mathrm{1}} \:=\:\mathrm{1},\:{x}_{\mathrm{2}} \:,\:{x}_{\mathrm{3}} \:,\:\ldots,\:{is}\:\:{a}\:\:{real}\:\:{numbers}\:\:{sequence}\:\:{for}\:\:{n}\:\geqslant\:\mathrm{1}\:\:{with}\:\: \\ $$$${recurrence}\:\:{relation}\:\:{x}_{{n}+\mathrm{1}} \:−\:{x}_{{n}} \:=\:\frac{\mathrm{1}}{\mathrm{2}{x}_{{n}} }\:\:. \\ $$$$\left[{x}\right]\:\:{is}\:\:{expressed}\:\:{as}\:\:{the}\:\:{largest}\:\:{integer}\:\:{of}\:\:{x}\:\:. \\ $$$$\left[\mathrm{25}{x}_{\mathrm{625}} \right]\:\:=\:\:? \\ $$