Question Number 143327 by SOMEDAVONG last updated on 13/Jun/21
$$\mathrm{1}/.\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{6}+\sqrt[{\mathrm{3}}]{\mathrm{6}+\sqrt[{\mathrm{3}}]{\mathrm{6}+..........+\sqrt[{\mathrm{3}}]{\mathrm{6}}}}}=? \\ $$
Answered by MJS_new last updated on 13/Jun/21
$${y}=\sqrt[{\mathrm{3}}]{\mathrm{6}+\sqrt[{\mathrm{3}}]{\mathrm{6}+...}} \\ $$$${y}^{\mathrm{3}} =\mathrm{6}+{y} \\ $$$${y}^{\mathrm{3}} −{y}+\mathrm{6}=\mathrm{0}\:\Rightarrow\:{y}=\mathrm{2} \\ $$