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Question Number 216917 by alcohol last updated on 24/Feb/25

$$li\underset{x\to +\mathrm{\infty }}{m}(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x}}}}-\sqrt{x})$$

Answered by mehdee7396 last updated on 24/Feb/25

$${lim}_{x\to \mathrm{\infty }}\frac{\sqrt{x+\sqrt{x+\sqrt{x}}}}{\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x}}}+\sqrt{x}}}$$$$={lim}_{x\to \mathrm{\infty }}\frac{\sqrt{x}}{2\sqrt{x}}=\frac{1}{2}$$$$$$

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