Question Number 216917 by alcohol last updated on 24/Feb/25
$${li}\underset{{x}\rightarrow+\infty} {{m}}\:\left(\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}−\sqrt{{x}}\right) \\ $$
Answered by mehdee7396 last updated on 24/Feb/25
$${lim}_{{x}\rightarrow\infty} \:\frac{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}{\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}+\sqrt{{x}}}} \\ $$$$={lim}_{{x}\rightarrow\infty} \:\frac{\sqrt{{x}}}{\:\mathrm{2}\sqrt{{x}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$