[latex] \lim_{n \to \infty} ( \sqrt[3]{3n} - \sqrt[3]{3n-1} )=[/latex]

[latex]lim_{n->\infty} (\sqrt[3]{n}-\sqrt[3]{n-1})=\\\\ lim_{n->\infty} \frac{(\sqr[3]{n}-\sqrt{n-1})(\sqrt[3]{n^2}+\sqrt[3]{n^2-n}+\sqrt[3]{(n-1)^2})}{\sqrt[3]{n^2}+\sqrt[3]{n^2-n}+\sqrt[3]{(n-1)^2}}=\\\\lim_{n->\infty} \frac{n-n+1}{\sqrt[3]{n^2}+\sqrt[3]{n^2-n}+\sqrt[3]{(n-1)^2}}=\frac{1}{\sqrt[3]{n^2}+\sqrt[3]{n^2-n}+\sqrt[3]{(n-1)^2}}=\\\\|\frac{1}{\infty}|=0[/latex]