\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" alt="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" align="absmiddle" class="latex-formula">