Question Number 109736 by mnjuly1970 last updated on 25/Aug/20
$$\:\:\:\:{please}\:{solve}\:: \\ $$$$\:\: \\ $$$${lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}\:+\sqrt{\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\sqrt[{\mathrm{4}}]{\mathrm{4}}\:+……\sqrt[{\mathrm{2}{n}}]{\mathrm{2}{n}}}{\mathrm{3}{n}−\mathrm{4}} \\ $$$$=??? \\ $$
Answered by Her_Majesty last updated on 25/Aug/20
$${for}\:{very}\:{high}\:{values}\:{of}\:{n}\:{almost}\:{all}\:{terms} \\ $$$$\sqrt[{{n}}]{{n}}\:{are}\:{equal}\:{to}\:\mathrm{1}\:\Rightarrow\:{we}\:{have}\:\sim\frac{\mathrm{2}{n}}{\mathrm{3}{n}−\mathrm{4}}\:{which} \\ $$$${is}\:{equal}\:{to}\:\frac{\mathrm{2}}{\mathrm{3}}\:{when}\:{n}\rightarrow\infty \\ $$