Question

$lim_{n to infty} ( sqrt[3]{3n} - sqrt[3]{3n-1} )=$

Answer 1

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