![image](https://tex.z-dn.net/?f=lim_%7Bn-%3E%5Cinfty%7D+%28%5Csqrt%5B3%5D%7Bn%7D-%5Csqrt%5B3%5D%7Bn-1%7D%29%3D%5C%5C%5C%5C+lim_%7Bn-%3E%5Cinfty%7D+%5Cfrac%7B%28%5Csqr%5B3%5D%7Bn%7D-%5Csqrt%7Bn-1%7D%29%28%5Csqrt%5B3%5D%7Bn%5E2%7D%2B%5Csqrt%5B3%5D%7Bn%5E2-n%7D%2B%5Csqrt%5B3%5D%7B%28n-1%29%5E2%7D%29%7D%7B%5Csqrt%5B3%5D%7Bn%5E2%7D%2B%5Csqrt%5B3%5D%7Bn%5E2-n%7D%2B%5Csqrt%5B3%5D%7B%28n-1%29%5E2%7D%7D%3D%5C%5C%5C%5Clim_%7Bn-%3E%5Cinfty%7D+%5Cfrac%7Bn-n%2B1%7D%7B%5Csqrt%5B3%5D%7Bn%5E2%7D%2B%5Csqrt%5B3%5D%7Bn%5E2-n%7D%2B%5Csqrt%5B3%5D%7B%28n-1%29%5E2%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bn%5E2%7D%2B%5Csqrt%5B3%5D%7Bn%5E2-n%7D%2B%5Csqrt%5B3%5D%7B%28n-1%29%5E2%7D%7D%3D%5C%5C%5C%5C%7C%5Cfrac%7B1%7D%7B%5Cinfty%7D%7C%3D0)
\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">