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


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Question Number 157660 by naka3546 last updated on 26/Oct/21

$G i v e n x_{1} = 1, x_{2}, x_{3}, \dots, i s a r e a l n u m b e r s s e q u e n c e f o r n ⩾ 1 w i t h$ $r e c u r r e n c e r e l a t i o n x_{n + 1} - x_{n} = \frac{1}{2 x_{n}} .$ $[x] i s e x p r e s s e d a s t h e l a r g e s t i n t e g e r o f x .$ $[25 x_{625}] = ?$
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